共查询到20条相似文献,搜索用时 46 毫秒
1.
The Main Conjecture on maximum distance separable (MDS) codes states that, except for some special cases, the maximum length of a q-ary linear MDS code of is q+1. This conjecture does not hold true for near maximum distance separable codes because of the existence of q-ary near-MDS elliptic codes having length bigger than q+1. An interesting related question is whether a near-MDS elliptic code may be extended to a longer near-MDS code. In this paper we prove some non-extendibility results for certain near-MDS elliptic codes. 相似文献
2.
Ferruh Özbudak Henning Stichtenoth 《Applicable Algebra in Engineering, Communication and Computing》2002,13(1):53-56
We present a simple construction of long linear codes from shorter ones. Our approach is related to the product code construction;
it generalizes and simplifies substantially the recent “Propagation Rule” by Niederreiter and Xing. Many optimal codes can
be produced by our method.
Received: June 23, 2000 相似文献
3.
4.
A new kind of Convolutional Codes generalizing Goppa Codes is proposed. This provides a systematic method for constructing convolutional codes with prefixed properties. In particular, examples of Maximum-Distance Separable (MDS) convolutional codes are obtained.This research was partially supported by the Spanish DGI through research project BFM2003-00078 and by the Junta de Castilla y León through research projects SA071/04 and SA032/02. 相似文献
5.
Tim Blackmore and Graham H. Norton introduced the notion of matrix-product codes over finite fields. The present paper provides
a generalization to finite chain rings. For codes a distance function is defined using a homogeneous weight function in the
ring. It is proved that the minimum distance of a matrix-product codes is determined by the minimum distances of the separate
codes. At the end of the paper we focus on Galois rings and define a special family of matrix-product codes.
相似文献
6.
We present a sheaf-theoretic setting for convolutional codes in that coherent sheaves (over a projective line) play the same
role as finite-dimensional linear spaces in the theory of block codes. Using coherent sheaves (and their cohomologies), we
give natural straightforward proofs of the main results on the structural properties of convolutional codes.
Received: May 7, 1999; revised version: August 11, 2000 相似文献
7.
B. Sundar Rajan M. U. Siddiqi 《Applicable Algebra in Engineering, Communication and Computing》1994,5(5):261-275
Cyclic codes with symbols from a residue class integer ringZ
m
are characterized in terms of the discrete Fourier transform (DFT) of codewords defined over an appropriate extension ring ofZ
m
. It is shown that a cyclic code of length n overZ
m
,n relatively prime tom, consists ofn-tuples overZ
m
having a specified set of DFT coefficients from the elements of an ideal of a subring of the extension ring. Whenm is equal to a product of distinct primes every cyclic code overZ
m
has an idempotent generator and it is shown that the idempotent generators can be easily identified in the transform domain. The dual code pairs overZ
m
are characterized in the transform domain for cyclic codes. Necessary and sufficient conditions for the existence of self-dual codes overZ
m
are obtained and nonexistence of self-dual codes for certain values ofm is proved. 相似文献
8.
Felice Manganiello 《Applicable Algebra in Engineering, Communication and Computing》2008,19(4):349-363
In this article, we illustrate an algorithm for the computation of the weight distribution of CRC codes. The recursive structure
of CRC codes will give us an iterative way to compute the weight distribution of their dual codes starting from some “representative”
words. Thanks to MacWilliams’ Theorem, the computation of the weight distribution of the dual codes can be easily brought
back to that of CRC codes.
The author was partially supported by the Swiss National Science Foundation under Grant no. 113251. 相似文献
9.
P. Langevin J. P. Zanotti 《Applicable Algebra in Engineering, Communication and Computing》1995,6(4-5):299-307
In this paper, we study particular linear codes defined overF
q
, with an astonishing property, their weight distribution is balanced, i.e. there is the same number of codewords for each nonzero weight of the code. We call these codesBWD-codes. We first study BWD-codes by means of the Pless identities and we completely characterize the two-weight projective case. We study the class of codes defined under subgroups of the multiplicative group ofF
q
s
, using the Gauss sums. Then, given a primep and an integerN dividingp – 1, we construct all theN-weight BWD-codes of that class. We conclude this paper by some tables of BWD-codes and an open problem. 相似文献
10.
We describe a construction of error-correcting codes on a fibration over a curve defined over a finite field, which may be
considered as a relative version of the classical Reed–Muller code. In the case of complete intersections in a projective
bundle, we give an explicit lower bound for the minimum distance. 相似文献
11.
Hideki Imai Manabu Hagiwara 《Applicable Algebra in Engineering, Communication and Computing》2008,19(3):213-228
In this paper, we give and explain some illustrative examples of research topics where error-correcting codes overlap with
cryptography. In some of these examples, error-correcting codes employed in the implementation of secure cryptographic protocols.
In the others, the codes are used in attacks against cryptographic schemes. Throughout this paper, we show the interrelation
between error-correcting codes and cryptography, as well as point out the common features and the differences between these
two fields. 相似文献
12.
Several results in coding theory (e.g. the Carlitz-Uchiyama bound) show that the weight distributions of certain algebraic codes of lengthn are concentrated aroundn/2 within a range of width n. It is proved in this article that the extreme weights of a linear binary code of sufficiently high dual distance cannot be too close ton/2, the gap being of order n. The tools used involve the Pless identities and the orthogonality properties of Krawtchouk polynomials, as well as estimates on their zeroes. As a by-product upper bounds on the minimum distance of self-dual binary codes are derived. 相似文献
13.
T. Aaron Gulliver Patric R.J. Östergård 《Applicable Algebra in Engineering, Communication and Computing》1998,9(2):153-159
In this paper, twenty new codes of dimension 6 are presented which give improved bounds on the maximum possible minimum distance
of quaternary linear codes. These codes belong to the class of quasi-twisted (QT) codes, and have been constructed using
a stochastic optimization algorithm, tabu search. A table of upper and lower bounds for d
4(n,6) is presented for n≤ 200.
Received: 20 December 1996 / Accepted: 13 May 1997 相似文献
14.
A. C. Lobstein V. A. Zinoviev 《Applicable Algebra in Engineering, Communication and Computing》1997,8(5):415-420
We present a new construction of binary nonlinear perfect codes with minimum distance 3 and lowerbound the number of nonequivalent
such codes.
Received: November 26, 1996; revised version: March 14, 1997 相似文献
15.
It is known that if a finite ring R is Frobenius then equivalences of linear codes over R are always monomial transformations. Among other results, in this paper we show that the converse of this result holds for finite local and homogeneous semilocal rings. Namely, it is shown that for every finite ring R which is a direct sum of local and homogeneous semilocal subrings, if every Hamming-weight preserving R-linear transformation of a codeC1 onto a code C2 is a monomial transformation then R is a Frobenius ring.Partially supported by Center of Ring Theory and Applications, Ohio University. 相似文献
16.
We construct extended classical Goppa codes that can have unrestricted block length. The parameters of the codes are estimated,
and the standard Berlekamp–Massey error processor is adapted to the codes.
Received: July 5, 1999; revised version: February 25, 2000 相似文献
17.
Mahadev S. Kolluru G. L. Feng T. R. N. Rao 《Applicable Algebra in Engineering, Communication and Computing》2000,10(6):433-464
Linear error-correcting codes, especially Reed-Solomon codes, find applications in communication and computer memory systems,
to enhance their reliability and data integrity. In this paper, we present Improved Geometric Goppa (IGG) codes, a new class
of error-correcting codes, based on the principles of algebraic-geometry. We also give a reasonably low complexity procedure
for the construction of these IGG codes from Klein curves and Klein-like curves, in plane and high-dimensional spaces. These
codes have good code parameters like minimum distance rate and information rate, and have the potential to replace the conventional
Reed-Solomon codes in most practical applications. Based on the approach discussed in this paper, it might be possible to
construct a class of codes whose performance exceeds the Gilbert-Varshamov bound.
Received: November 14, 1995; revised version: November 22, 1999 相似文献
18.
Y. Kaipainen K. Suominen 《Applicable Algebra in Engineering, Communication and Computing》1997,8(5):403-410
We study S. D. Cohen’s method of estimating the covering radius of long primitive non-binary BCH codes with prime field alphabet.
As an application we show that the covering radius is at most 7 for long 5-ary BCH codes with minimum distance seven.
Received: November 13, 1996; revised version: March 11, 1997 相似文献
19.
Justo Peralta Blas Torrecillas 《Applicable Algebra in Engineering, Communication and Computing》2002,13(2):107-120
Since S.D. Berman showed in 1967 that cyclic codes and Reed Muller codes can be studied as ideals in a group algebra KG (over a finite field K and G is considered, in each case, a finite cyclic group and a 2-group respectively), several authors have investigated these codes.
It has been observed, that the presence of additional algebraic structure make their study more effective. Following these
ideas, we consider codes which are (graded) left ideals of a graded ring R or more generally, codes as (graded) left R-modules. In this paper, a linear code is graded if it is a graded R-module for some multiplicative group G and a G-graded K-algebra R. We will show that some important properties of graded codes can be obtained from their homogeneous components and then we
generalize some results about codes as ideals in group algebras. In particular, we study cocyclic codes as ideals in a twisted
group algebra, and more generally, in a crossed product.
Received: May 22, 1999; revised version: August 20, 2001 相似文献
20.
I. M. Duursma C. Rentería H. Tapia-Recillas 《Applicable Algebra in Engineering, Communication and Computing》2001,11(6):455-462
By using results and techniques from commutative algebra such as the vanishing ideal of a set of points, its a-invariant, the Hilbert polynomial and series, as well as finite free resolutions and the canonical module, some results about
Reed-Muller codes defined on a zero-dimensional complete intersection in the n-projective dimensional space are given. Several examples of this class of codes are presented in order to illustrate the
ideas.
Received: March 11, 1999; revised version: November 6, 2000 相似文献