A formula on the weight distribution of linear codes with applications to AMDS codes

被引：5

作者：

Meneghetti, Alessio ^{[1
]}

Pellegrini, Marco ^{[2
]}

Sala, Massimiliano ^{[1
]}

机构：

[1] Univ Trento, Dept Math, Trento, Italy

[2] Univ Florence, Dept Math & Comp Sci, Florence, Italy

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2022年 / 77卷

关键词：

Weight distribution; Linear codes; AMDS codes; Extremal codes; GLEASONS THEOREM; ERROR; ENUMERATORS; PROBABILITY; CODEWORDS; DISTANCE;

D O I：

10.1016/j.ffa.2021.101933

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The determination of the weight distribution of linear codes has been a fascinating problem since the very beginning of coding theory. There has been a lot of research on weight enumerators of special cases, such as self-dual codes and codes with small Singleton's defect. We propose a new set of linear relations that must be satisfied by the coefficients of the weight distribution. From these relations we are able to derive known identities (in an easier way) for interesting cases, such as extremal codes, Hermitian codes, MDS and NMDS codes. Moreover, we are able to present for the first time the weight distribution of AMDS codes. We also discuss the link between our results and the Pless equations. (c) 2021 Elsevier Inc. All rights reserved.

引用

页数：15

共 36 条

[1] [Anonymous], 2006, INT J MATH MATH SCI, DOI DOI 10.1124/JPET.106.111807
[2] The weight hierarchy of Hermitian codes
Barbero, AI
Munuera, C
[J]. SIAM JOURNAL ON DISCRETE MATHEMATICS, 2000, 13 (01) : 79 - 104
[3] Bellini Emanuele, 2018, INT J INF CODING, V5, P18
[4] GLEASONS THEOREM ON SELF-DUAL CODES
BERLEKAMP, ER
SLOANE, NJA
MACWILLIAMS, FJ
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 1972, 18 (03) : 409 - +
[5] THE LINEAR ALGEBRA OF THE PASCAL MATRIX
BRAWER, R
PIROVINO, M
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1992, 174 : 13 - 23
[6] Cary Huffman W., 2010, FUNDAMENTALS ERROR C
[7] CHANG SC, 1980, IEEE T INFORM THEORY, V26, P476, DOI 10.1109/TIT.1980.1056212
[8] De Boer M. A., 1996, Designs, Codes and Cryptography, V9, P143
[9] Dodunekov S., 1995, J GEOM, V54, P30
[10] Extremal weight enumerators and ultraspherical polynomials
Duursma, I
[J]. DISCRETE MATHEMATICS, 2003, 268 (1-3) : 103 - 127

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