等重码的一些新结果

本文给出两种构造二元非线性等重码的方法，这些方法是［１］文构造二元非线性循环等重码方法的改进。通过我们的构造方法可以得到几类二元最优等重码。我们进一步说明通过ＧＦ（ｑ）上的等重码和达到Ｐｌｏｔｋｉｎ界的最优码可以构造达到Ｊｏｈｎｓｏｎ上界的二元最优等重码     

Cyclotomic optical orthogonal codes of composite lengths

Optical orthogonal codes (OOCs) have applications in optical code-division multiple-access communications systems and other wideband code-division multiple environments. They can also be used to construct protocol sequences for multiuser collision channel without feedback, and constant-weight codes for error detection and correction. We have given a cyclotomic construction of several classes of (2/sup m/-1,w,2) OOCs recently. The purpose of this paper is to present five classes of (q-1,w,2) OOCs, and thus five classes of binary constant-weight cyclic codes, where q is a power of an odd prime.     

The worst case probability of undetected error for linear codes onthe local binomial channel

The worst case probability of undetected error for a linear [n,k:q] code used on a local binomial channel is studied. For the two most important cases it is determined in terms of the weight hierarchy of the code. The worst case probability of undetected error is determined explicitly for some classes of codes     

Maximalq-nary linear codes with large minimum distance (Corresp.)

This correspondence presents a complete solution to the problem of constructing maximalq-nary codes, for any word lengthnand minimum distancedin the regionqd geq (q - 1)n. Several interesting results regarding the interdependence of these codes are developed, which reveal the unique structure of the code spaces of the regionqd geq (q - 1)n. Some new maximal codes are obtained for the regionqd < (q - 1)n.     

Linear generalised concatenated codes over ring Z/sub q/

A method for constructing linear codes over the ring of integers modulo q, Z/sub q/, using the idea of generalised concatenated (GC) codes is presented.<>     

几类指标为2的不可约拟循环码的重量分布

少重量线性码在认证码、结合方案以及秘密共享方案的构造中有着重要的应用。如何构造少重量线性码一直是编码理论研究的重要内容。该文通过选取特殊的定义集,构造了有限域上指标为2的不可约拟循环码,利用有限域上的高斯周期确定了几类指标为2的不可约拟循环码的重量分布,并且得到了几类2-重量线性码和3-重量线性码。结果表明,由该文构造的3类2-重量线性码中有两类是极大距离可分(MDS)码,另一类达到了Griesmer界。     

等重码的约翰逊界和格雷厄姆界的几点注记

本文给出了四类达到约翰逊上界的等重码和两类超过格雷厄姆下界的等重码。     

一种基于伪循环MDS码的准循环LDPC码构造方法

该文提出了一种利用两个信息符号的伪循环最大距离可分(MDS)码,构造围长为6的准循环低密度奇偶校验(LDPC)码的方法。在GF(q)中,它通过直接计算长为q+1的伪循环MDS码生成多项式,构造准循环LDPC码的校验矩阵。其主要利用了含两个信息符号的伪循环MDS码字特殊的循环性,及任意两个码字间距离不小于q的特点,使所构造的准循环LDPC码保证无4环。仿真结果表明,基于伪循环MDS码的准循环LDPC码在高斯信道下,能获得较好的误码性能。     

A characterization of MMD codes

Let C be a linear [n,k,d]-code over GF(q) with k⩾2. If s=n-k+1-d denotes the defect of C, then by the Griesmer bound, d⩽(s+1)q. Now, for obvious reasons, we are interested in codes of given defect s for which the minimum distance is maximal, i.e., d=(s+1)q. We classify up to formal equivalence all such linear codes over GF(q). Remember that two codes over GF(q) are formally equivalent if they have the same weight distribution. It turns out that for k⩾3 such codes exist only in dimension 3 and 4 with the ternary extended Golay code, the ternary dual Golay code, and the binary even-weight code as exceptions. In dimension 4 they are related to ovoids in PG(3,q) except the binary extended Hamming code, and in dimension 3 to maximal arcs in PG(2,q)     

有限域上常循环厄密特对偶包含码及其应用

该文研究了有限域GF(q2)上长度为(q2m-1)/(q2-1)的常循环码。给出一类常循环码是厄米特对偶包含码的一个充要条件,并确定了这类常循环厄米特对偶包含码的参数。利用厄米特构造,得到了比量子BCH码参数更好的量子纠错码。     

NOTE ON THE JOHNSON''''S BOUNDS AND GRAHAM''''S BOUNDS FOR CONSTANT WEIGHT CODES

This paper presents four classes of codes which meet the Johnson's upper bound and twoclasses of codes which have gone beyond the Graham's lower bound.     

On algebraic construction of Gallager and circulant low-density parity-check codes

This correspondence presents three algebraic methods for constructing low-density parity-check (LDPC) codes. These methods are based on the structural properties of finite geometries. The first method gives a class of Gallager codes and a class of complementary Gallager codes. The second method results in two classes of circulant-LDPC codes, one in cyclic form and the other in quasi-cyclic form. The third method is a two-step hybrid method. Codes in these classes have a wide range of rates and minimum distances, and they perform well with iterative decoding.     

Codes correcting a single insertion/deletion of a zero or a singlepeak-shift

Codes of (d,k) sequences of constant Hamming weight are considered. Perfect codes correcting a single insertion, deletion, or peak-shift are defined and shown to exist. A systematic method to construct large classes of perfect codes is given. A number of related problems are considered     

Number of information symbols in polynomial codes

Polynomial codes and their dual codes as introduced by Kasami, Lin, and Peterson have considerable algebraic and geometric structure. It has been shown that these codes contain many well-known classes of cyclic codes as subclasses, such as BCH codes, projective geometry codes (PG codes), Euclidean geometry codes (EG codes), and generalized Reed-Muller codes (GRM codes). In this paper, combinatorial expressions for the number of information symbols and parity-check symbols in polynomial codes are derived. The results are applied to two important subclasses of codes, the PG codes and EG codes.     

List decoding of q-ary Reed-Muller codes

The q-ary Reed-Muller (RM) codes RM/sub q/(u,m) of length n=q/sup m/ are a generalization of Reed-Solomon (RS) codes, which use polynomials in m variables to encode messages through functional encoding. Using an idea of reducing the multivariate case to the univariate case, randomized list-decoding algorithms for RM codes were given in and . The algorithm in Sudan et al. (1999) is an improvement of the algorithm in , it is applicable to codes RM/sub q/(u,m) with u相似文献   

Explicit construction of families of LDPC codes with no 4-cycles

Low-density parity-check (LDPC) codes are serious contenders to turbo codes in terms of decoding performance. One of the main problems is to give an explicit construction of such codes whose Tanner graphs have known girth. For a prime power q and m/spl ges/2, Lazebnik and Ustimenko construct a q-regular bipartite graph D(m,q) on 2q/sup m/ vertices, which has girth at least 2/spl lceil/m/2/spl rceil/+4. We regard these graphs as Tanner graphs of binary codes LU(m,q). We can determine the dimension and minimum weight of LU(2,q), and show that the weight of its minimum stopping set is at least q+2 for q odd and exactly q+2 for q even. We know that D(2,q) has girth 6 and diameter 4, whereas D(3,q) has girth 8 and diameter 6. We prove that for an odd prime p, LU(3,p) is a [p/sup 3/,k] code with k/spl ges/(p/sup 3/-2p/sup 2/+3p-2)/2. We show that the minimum weight and the weight of the minimum stopping set of LU(3,q) are at least 2q and they are exactly 2q for many LU(3,q) codes. We find some interesting LDPC codes by our partial row construction. We also give simulation results for some of our codes.     

Bit-error bounds for trellis-coded MPSK in mixed fading channels

Bit-error probability (BEP) bounds of trellis-coded MPSK systems over two classes of mixed fading channels are studied. These two classes of channels have been proposed as candidate models for mobile satellite communications. The first class consists of slow and frequency-nonselective fading channels whose output field strengths follow a probability law characterized by a convex combination of Rician and Rayleigh/lognormal distributions. For the other class of fading channels, the received signal amplitude has a convex combination of Rician and Rician/lognormal distributions. We analyze performance bounds for trellis codes that belong to the class of either geometrically uniform codes (GUCs) or quasi-regular codes (QRCs). Receivers with either ideal channel state information (CSI) or no CSI at all are considered. We examine asymptotic behaviors of these codes and identify key design parameters. Numerical results are provided to illustrate and compare the BEP performances of various codes and to validate the usefulness of the asymptotic analysis     

On robust and dynamic identifying codes

A subset C of vertices in an undirected graph G=(V,E) is called a 1-identifying code if the sets I(v)={u/spl isin/C:d(u,v)/spl les/1}, v/spl isin/V, are nonempty and no two of them are the same set. It is natural to consider classes of codes that retain the identification property under various conditions, e.g., when the sets I(v) are possibly slightly corrupted. We consider two such classes of robust codes. We also consider dynamic identifying codes, i.e., walks in G whose vertices form an identifying code in G.     

Integrating voice and data applications in T/CDMA architectures

This letter analyzes the behavior of two time-code division architectures serving voice and data applications on the uplink of a cellular radio system. Both solutions attribute speech users one code over a timeslot, whereas data users are granted several codes over the same timeslot or a single code over several time slots. Call admission control dynamically attributes resources if specified levels of transmission quality are met. The blocking probability of the two classes of users is determined, demonstrating that the multicode T/CDMA approach performs better than the multislot solution and than a pure CDMA system