On the minimum distance of Castle codes

被引：6

作者：

Olaya-Leon, Wilson ^{[1
,3
]}

Munuera, Carlos ^{[2
]}

机构：

[1] Univ Ind Santander, Escuela Matemat, Bucaramanga 678, Colombia

[2] Univ Valladolid, Dept Appl Math, Valladolid 47014, Spain

[3] Univ Valladolid, Dept Algebra, Valladolid 47014, Spain

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2013年 / 20卷

关键词：

Error-correcting codes; AG codes; Castle curves; Castle codes; Minimum distance; Order bound; BOUNDS;

D O I：

10.1016/j.ffa.2012.12.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Castle codes are algebraic geometry one-point codes on Castle curves. This family contains some of the most important AG codes among those studied in the literature to date. The minimum distance of these codes can be bounded by using the order-like bound d*, which is known to be equivalent to the classical order bound when both can be applied. In this paper we compute d* for some Castle codes, including those related to semigroups generated by two elements and telescopic semigroups. In particular we compute the bound d* in full for Suzuki codes. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：55 / 63

页数：9

共 50 条

[1] ON THE MINIMUM DISTANCE OF CYCLIC CODES
VANLINT, JH
WILSON, RM
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 1986, 32 (01) : 23 - 40
[2] On the minimum distance of turbo codes
Truhachev, D
Lentmaier, M
Wintzell, O
Zigangirov, KS
[J]. ISIT: 2002 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, PROCEEDINGS, 2002, : 84 - 84
[3] MINIMUM DISTANCE OF ELLIPTIC CODES
SHOKROLLAHI, MA
[J]. ADVANCES IN MATHEMATICS, 1992, 93 (02) : 251 - 281
[4] MINIMUM POLARIZED DISTANCE CODES
MARCUS, MP
[J]. IBM JOURNAL OF RESEARCH AND DEVELOPMENT, 1961, 5 (03) : 241 - 248
[5] ON THE MINIMUM DISTANCE OF COMBINATORIAL CODES
TOLHUIZEN, L
VANLINT, JH
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 1990, 36 (04) : 922 - 923
[6] On the minimum distance of array codes as LDPC codes
Yang, KC
Helleseth, T
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2003, 49 (12) : 3268 - 3271
[7] A new bound on the minimum distance of cyclic codes using small-minimum-distance cyclic codes
Zeh, Alexander
Bezzateev, Sergey
[J]. DESIGNS CODES AND CRYPTOGRAPHY, 2014, 71 (02) : 229 - 246
[8] A new bound on the minimum distance of cyclic codes using small-minimum-distance cyclic codes
Alexander Zeh
Sergey Bezzateev
[J]. Designs, Codes and Cryptography, 2014, 71 : 229 - 246
[9] Minimum distance and the minimum weight codewords of Schubert codes
Ghorpade, Sudhir R.
Singh, Prasant
[J]. FINITE FIELDS AND THEIR APPLICATIONS, 2018, 49 : 1 - 28
[10] A NOTE ON THE MINIMUM DISTANCE OF HERMITIAN CODES
邢朝平
[J]. Science Bulletin, 1992, (02) : 95 - 99

← 1 2 3 4 5 →