Optimal binary and ternary linear codes with hull dimension one

被引：7
|
作者：
Mankean, Todsapol [1 ]
Jitman, Somphong [1 ]
机构：
[1] Silpakorn Univ, Fac Sci, Dept Math, Amphoe Muang 73000, Nakhon Pathom, Thailand
来源：
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING | 2020年 / 64卷 / 1-2期
关键词：
Linear codes; Optimal linear codes; Griesmer bound; Euclidean inner product; Hermitian inner product; Hulls; Hull dimensions; LCD CODES; PERMUTATION; EQUIVALENT;
D O I：
10.1007/s12190-020-01348-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Hulls of linear codes have been of interest and extensively studied due to their wide applications. In this paper, we focus on constructions and optimality of linear codes with hull dimension one over small finite fields. General constructions for such codes are given together with the analysis on their parameters. Optimal linear [n, 2, d](q) codes with hull dimension one are presented for all positive integers n >= 3 and q is an element of {2, 3}. Moreover, for q = 2, the enumeration of such optimal codes is given up to equivalence.
引用
收藏
页码：137 / 155
页数：19
相关论文
共 50 条
  • [1] Optimal binary and ternary linear codes with hull dimension one
    Todsapol Mankean
    Somphong Jitman
    [J]. Journal of Applied Mathematics and Computing, 2020, 64 : 137 - 155
  • [2] Characterization and classification of optimal ternary linear one-dimensional hull codes
    Tong, Tingting
    Li, Shitao
    Shi, Minjia
    [J]. JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2024, : 5557 - 5574
  • [3] ON OPTIMAL TERNARY LINEAR CODES OF DIMENSION 6
    Maruta, Tatsuya
    Oya, Yusuke
    [J]. ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2011, 5 (03) : 505 - 520
  • [4] Optimal binary linear codes of dimension at most seven
    Bouyukliev, I
    Jaffe, DB
    [J]. DISCRETE MATHEMATICS, 2001, 226 (1-3) : 51 - 70
  • [5] Improvements to the founds on optimal ternary linear codes of dimension 6
    Gulliver, TA
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 1997, 43 (05) : 1632 - 1638
  • [6] NEW OPTIMAL TERNARY LINEAR CODES OF DIMENSION-6
    GULLIVER, TA
    [J]. ARS COMBINATORIA, 1995, 40 : 97 - 108
  • [7] Constructions and bounds on quaternary linear codes with Hermitian hull dimension one
    Mankean, Todsapol
    Jitman, Somphong
    [J]. ARABIAN JOURNAL OF MATHEMATICS, 2021, 10 (01) : 175 - 184
  • [8] Constructions and bounds on quaternary linear codes with Hermitian hull dimension one
    Todsapol Mankean
    Somphong Jitman
    [J]. Arabian Journal of Mathematics, 2021, 10 : 175 - 184
  • [9] OPTIMAL BINARY HIERARCHICAL POSET CODE HAVING HULL DIMENSION ONE
    More, Rohini Baliram
    Marka, Venkatrajam
    [J]. ADVANCES AND APPLICATIONS IN DISCRETE MATHEMATICS, 2024, 41 (03): : 239 - 259
  • [10] Binary optimal linear codes with various hull dimensions and entanglement-assisted QECCs
    Jon-Lark Kim
    [J]. Computational and Applied Mathematics, 2023, 42
12345