The nonexistence of near-extremal formally self-dual codes

被引：11
|
作者：
Han, Sunghyu [1 ]
Kim, Jon-Lark [2 ]
机构：
[1] Ewha Womans Univ, Inst Math Sci, Dept Math, Seoul 120750, South Korea
[2] Univ Louisville, Dept Math, Louisville, KY 40292 USA
来源：
DESIGNS CODES AND CRYPTOGRAPHY | 2009年 / 51卷 / 01期
关键词：
Extremal codes; Formally self-dual codes; Near-extremal codes; Self-dual codes; BOUNDS;
D O I：
10.1007/s10623-008-9244-0
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
A code C is called formally self-dual if C and C-perpendicular to have the same weight enumerators. There are four types of nontrivial divisible formally self-dual codes over F-2, F-3, and F-4. These codes are called extremal if their minimum distances achieve the Mallows-Sloane bound. S. Zhang gave possible lengths for which extremal self-dual codes do not exist. In this paper, we define near-extremal formally self-dual (f.s.d.) codes. With Zhang's systematic approach, we determine possible lengths for which the four types of near-extremal formally self-dual codes as well as the two types of near-extremal formally self-dual additive codes cannot exist. In particular, our result on the nonexistence of near-extremal binary f.s.d. even codes of any even length n completes all the cases since only the case 8 vertical bar n was dealt with by Han and Lee.
引用
收藏
页码：69 / 77
页数：9
相关论文
共 50 条
  • [11] On the Classification of Extremal Even Formally Self-Dual Codes
    J. E. Fields
    P. Gaborit
    W. C. Huffman
    V. Pless
    [J]. Designs, Codes and Cryptography, 1999, 18 : 125 - 148
  • [12] CLASSIFICATION OF THE EXTREMAL FORMALLY SELF-DUAL EVEN CODES OF LENGTH 30
    Bouyuklieva, Stefka
    Bouyukliev, Iliya
    [J]. ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2010, 4 (03) : 433 - 439
  • [13] Classification of Extremal Double Circulant Formally Self-Dual even Codes
    Gulliver T.A.
    Harada M.
    [J]. Designs, Codes and Cryptography, 1997, 11 (1) : 25 - 35
  • [14] Classification of Extremal Formally Self-Dual Even Codes of Length 22
    Masaaki Harada
    Patric R.J. Östergård
    [J]. Graphs and Combinatorics, 2002, 18 : 507 - 516
  • [15] Classification of extremal formally self-dual even codes of length 22
    Harada, M
    Östergård, PRJ
    [J]. GRAPHS AND COMBINATORICS, 2002, 18 (03) : 507 - 516
  • [16] NEW EXTREMAL FORMALLY SELF-DUAL EVEN CODES OF LENGTH 30
    Harada, Masaaki
    Waki, Katsushi
    [J]. ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2009, 3 (04) : 311 - 316
  • [17] Nonexistence of extremal doubly even self-dual codes with large length
    Ma, XR
    [J]. DISCRETE MATHEMATICS, 1998, 185 (1-3) : 265 - 274
  • [18] Constructions of self-dual codes and formally self-dual codes over rings
    Dougherty, Steven T.
    Kaya, Abidin
    Salturk, Esengul
    [J]. APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2016, 27 (05) : 435 - 449
  • [19] Constructions of self-dual codes and formally self-dual codes over rings
    Steven T Dougherty
    Abidin Kaya
    Esengül Saltürk
    [J]. Applicable Algebra in Engineering, Communication and Computing, 2016, 27 : 435 - 449
  • [20] On the classification of extremal even formally self-dual codes of lengths 20 and 22
    Fields, JE
    Gaborit, P
    Huffman, WC
    Pless, V
    [J]. DISCRETE APPLIED MATHEMATICS, 2001, 111 (1-2) : 75 - 86
12345