Large families of quaternary sequences with low correlation

A family of quaternary (Z₄-alphabet) sequences of length L=2^r-1, size M⩾L²+3L+2, and maximum nontrivial correlation parameter C_max⩽2√(L+1)+1 is presented. The sequence family always contains the four-phase family 𝒜. When r is odd, it includes the family of binary Gold sequences. The sequence family is easily generated using two shift registers, one binary, the other quaternary. The distribution of correlation values is provided. The construction can be extended to produce a chain of sequence families, with each family in the chain containing the preceding family. This gives the design flexibility with respect to the number of intermittent users that can be supported, in a code-division multiple-access cellular radio system. When r is odd, the sequence families in the chain correspond to shortened Z₄-linear versions of the Delsarte-Goethals codes     

New lower bounds for covering codes

Some new lower bounds on |C| for a binary linear [n, k]R code C with n+1=t(R +1)-r(0⩽r<R+1, t>2 odd) or with n+1=t(R+1)-1(t>2 even) are obtained. These bounds improve the sphere covering bound considerably and give several new values and lower bounds for the function t[n, k], the smallest covering radius of any [n, k] code     

Generalized Hamming weights of linear codes

The generalized Hamming weight, d_r(C), of a binary linear code C is the size of the smallest support of any r-dimensional subcode of C. The parameter d_r(C) determines the code's performance on the wire-tap channel of Type II. Bounds on d_r(C), and in some cases exact expressions, are derived. In particular, a generalized Griesmer bound for d_r(C) is presented and examples are given of codes meeting this bound with equality     

Overshoot-controlled RLC interconnections

How overshoot in the step response of a circuit involving an RLC line can be controlled using a combination of driver and line resistance that depends on the load capacitance is shown. The no-peak condition or its equivalent is used to relate line parameters to the driver and load impedances. This no-peak condition generalizes the impedance matching customarily used for lossless lines, i.e. it provides an alternative to the traditional choice R_D=√ L/C. The results allow improved circuit response without risk of overshoot, for example, by reduction of driver resistance below √L/C for cases where line resistance is unavoidable and/or where load capacitance is not negligible compared to line capacitance. The algebraic formulas derived are more effective than case-by-case numerical simulations for analyzing scaling and technology issues, whether on-chip, or at the packaging, board, or system levels     

Binary [18,11]2 codes do not exist-Nor do [64,53]2 codes

A binary, linear block code C with block length n and dimension n is commonly denoted by [n, k] or, if its minimum distance is d, by [n, k,d]. The code's covering radius r(C) can be defined as the smallest number r such that any binary column vector of length (n-k) can be written as a sum of r or fewer columns of a parity-check matrix of C. An [n,k] code with covering radius r is denoted by [n,k]r. R.A. Brualdi et al., (1989) showed that l(m,r) is defined to be the smallest n such that an [n,n-m]r code exists. l(m,2) is known for m⩽6, while it is shown by Brualdi et al. that 17⩽l(7,2)⩽19. This lower bound is improved by A.R. Calderbank et al. (1988), where it is shown that [17,10]2 codes do not exist. The nonexistence of [18,11]2 codes is proved, so that l(7,2)=19. l[7.2)=19 is established by showing that [18,11]2 codes do not exist. It is also shown that [64,53]2 codes do not exist, implying that l(11,2)⩾65     

A new family of binary pseudorandom sequences having optimalperiodic correlation properties and larger linear span

A collection of families of binary {0,1} pseudorandom sequences is introduced. Each sequence within a family has period N=2"-1, where n=2m is an even integer. There are 2^m sequences within a family, and the maximum overall (nontrivial) auto- and cross-correlation values equals 2^m+1. Thus, these sequences are optimal with respect to the Welch bound on the maximum correlation value. Each family contains a Gordon-Mills-Welch (GMW) sequence, and the collection of families includes as a special case the small set of Kasami sequences. The linear span of these sequences varies within a family but is always greater than or equal to the linear span of the GMW sequence contained within the family. Exact closed-form expressions for the linear span of each sequence are given. The balance properties of such families are evaluated, and a count of the number of distinct families of given period N that can be constructed is provided     

Optimal biphase sequences with large linear complexity derived fromsequences over Z4

New families of biphase sequences of size 2^r-1+1, r being a positive integer, are derived from families of interleaved maximal-length sequences over Z₄ of period 2(2^r-1). These sequences have applications in code-division spread-spectrum multiuser communication systems. The families satisfy the Sidelnikov bound with equality on &thetas;_max, which denotes the maximum magnitude of the periodic cross-correlation and out-of-phase autocorrelation values. One of the families satisfies the Welch bound on &thetas;_max with equality. The linear complexity and the period of all sequences are equal to r(r+3)/2 and 2(2 ^r-1), respectively, with an exception of the single m-sequence which has linear complexity r and period 2^r-1. Sequence imbalance and correlation distributions are also computed     

On balanced codes

In a balanced code each codeword contains equally many 1's and 0's. Parallel decoding balanced codes with 2^r (or 2^r -1) information bits are presented, where r is the number of check bits. The 2²-r-1 construction given by D.E. Knuth (ibid., vol.32, no.1, p.51-3, 1986) is improved. The new codes are shown to be optimal when Knuth's complementation method is used     

Integrated reactive components in power electronic circuits

Methods of integrating capacitive and inductive components into new compact devices are presented. Configurations for integrating various combinations of L-C networks are shown. A example of the construction of an integrated L-C for a series-resonant converter is evaluated both practically and experimentally     

On the [24, 12, 10] quaternary code and binary codes with anautomorphism having two cycles

A general decomposition theorem is given for codes over finite fields which have an automorphism of a given type. Such codes can be decomposed as direct sums of subcodes which may be viewed as shorter length codes over extension fields. If such a code is self-dual, sometimes the subcodes are also. This decomposition is applied to prove that the self-dual [24, 12, 10] quaternary code has no automorphism of order 3. This decomposition is also applied to count the number of equivalent [2r, r] and [2r+2r+1] self-dual binary codes with an automorphism of prime order r     

Short codes with a given covering radius

The covering radius r of a code is the maximum distance from any vector in the space containing the code to the nearest codeword. The authors introduce a new function l(m,r), called the length function, which equals the smallest length of a binary code of codimension m and covering radius r. They investigate basic properties of the length function. Projective geometries over larger fields are used to construct families of codes which improve significantly the upper bound for l(m,2) obtained by amalgamation of Hamming codes. General methods are developed for ruling out the existence of codes of covering radius 2 with a given codimension and length resulting in lower bounds for l(m,2). A table is presented which gives the best results now known for l(m,r) with m⩽12 and r⩽12     

On the Hamming distance properties of group codes

Under certain mild conditions, the minimum Hamming distance D of an (N, K, D) group code C over a non-abelian group G is bounded by D⩽N -2K+2 if K⩽N/2, and is equal to 1 if K>N/2. Consequently, there exists no (N, K, N-K+1) group code C over an non-abelian group G if 1<K<N. Moreover, any normal code C with a non-abelian output space has minimum Hamming distance equal to D=1. These results follow from the fact that non-abelian groups have nontrivial commutator subgroups. Finally, if C is an (N, K, D) group code over an abelian group G that is not elementary abelian, then there exists an (N, K, D) group code over a smaller elementary abelian group G'. Thus, a group code over a general group G cannot have better parameters than a conventional linear code over a field of the same size as G     

Constructions of error-correcting DC-free block codes

Two DC-free codes are presented with distance 2d, b ⩾1 length 2n+2r(d-1) for d⩽3 and length 2n+2r(d-1)(2d -1) for d>3, where r is the least integer ⩾log₂ (2n+1). For the first code l=4, c=2, and the asymptotic rate of this code is 0.7925. For the second code l=6, c=3, and the asymptotic rate of this code is 0.8858. Asymptotically, these rates achieve the channel capacity. For small values of n these codes do not achieve the best rate. As an example of codes of short length with good rate, the author presents a (30, 10, 6, 4) DC-free block code with 2²¹ codewords. A construction is presented for which from a given code C ₁ of length n, even weight, and distance 4, the author obtains a (4n, l, c, 4) DC-free block code C₂, where l is 4, 5 or 6, and c is not greater than n+1 (but usually significantly smaller). The codes obtained by this method have good rates for small lengths. The encoding and decoding procedures for all the codes are discussed     

On linear inductance- and capacitance-time conversions usingNIC-type configurations

The problem of linear inductance- and capacitance-time (L/T, C/T) conversion is approached through the systematic study of four approaches to building astable multivibrators using piecewise linear resistances obtained from one operational amplifier (OA) negative impedance converter (NIC) configuration. A new L/T converter with grounded inductance is found. Formulas for the time period taking into consideration the losses as well as the OA saturation output resistance are derived     

MOS flat-band capacitance method at low temperatures

The expression C_FB=C_ox×(ϵ_si /L_D)/[C_ox+(ϵ_si /L_D)] (where L_D is the Debye length), commonly used for the flatband capacitance of the MOS structure, is invalid in the temperature range below 100 K. Consequently, significant error may be encountered when the flatband capacitance method is used to extract the flatband voltage, V _FB, which is of considerable interest for both the modeling and characterization of MOS devices. To extend this method to low-temperature CMOS applications one has to use a more general model that can be obtained by applying Fermi-Dirac statistics and taking into account the impurity freeze-out effect. It is shown that when the temperature dependence of V_FB is extracted using this approach, the experimental data for n⁺ polysilicon gate MOS capacitors are in good agreement with a simple method     

Generalized Kasami Sequences: The Large Set

In this correspondence, new binary sequence families F^k of period 2ⁿ-1 are constructed for even n and any k with gcd(k,n)=2 if n/2 is odd or gcd(k,n)=1 if n/2 is even. The distribution of their correlation values is completely determined. These families have maximum correlation 2^n/2+1 and family size 2^3n/2 + 2^n/2 for odd n/2 or 2^3n/2+2^n/2-1 for even n/2. The proposed families include the large set of Kasami sequences, where the k is taken as k=n/2+1.     

Optical orthogonal codes-new bounds and an optimal construction

A technique for constructing optimal OOCs (optical orthogonal codes) is presented. It provides the only known family of optimal (with respect to family size) OOCs having λ=2. The parameters (n ,ω,λ) are respectively (p^2m-1, p^m+1,2), where p is any prime and the family size is p^m-2. Three distinct upper bounds on the size of an OOC are presented that, for many values of the parameter set (n,ω,λ), improve upon the tightest previously known bound     

A model for fast switching transients in power systems: the nearzone concept

The author presents a simple time-domain model which makes it possible to predict the order of magnitude of the highest di/ dt values generated by closing switches in electrical power systems. The model is based on traveling-wave analysis. It is demonstrated that two different approaches must be applied, according to whether (a) the closing time, T_s, of the switch is faster than twice the traveling time to the first reflection point or (b) T_s is much slower. Under condition (b) the well-known quasistationary approach di/dt_max=U₀/L can be used, where U₀ is the switched voltage and L is the self-inductance of the line between the stray capacitances located to the left and the right of the switching device. Under condition (a) a new formula must be applied: di/dt _max≈2 U₀/ZT_s, where Z is the line impedance of the line in which the switching device is installed and T_s is the time during which the voltage across the switch collapses from U₀ to zero. Experimental results are given from both fast and slow closing switches     

Some results on the norm of codes

Two upper bounds for the norm N(C) of a binary linear code C with minimal weight d and covering radius R are given. The second of these bounds implies that C is normal if R=3     

The inductance matrix of a multiconductor transmission line inmultiple magnetic media

A simple relationship between the inductance matrix and the auxiliary capacitance matrix is given. For a multiconductor transmission line consisting of N_c conducting cylinders in inhomogeneous media consisting of N_d homogeneous regions with permeabilities μ_i and permittivities ϵ _i, the inductance matrix [L] for the line is obtained by solving the magnetostatic problem of N_c conductors in N_d regions with permeabilities μ _i. The capacitance matrix [C] for the line is obtained by solving the electrostatic problem of N_c conductors in N_d regions with permittivities ϵ _i. It is shown that [L]=μ₀ϵ₀[C^'] ^-1, where [C^'] is the capacitance matrix of an auxiliary electrostatic problem of N_c conductors in N_d regions with relative permittivities set equal to the reciprocals of the relative permeabilities of the magnetostatic problem, i.e. ϵ^' _i/ϵ₀=μ₀/μ_i