Optimal Two-Weight Codes From Trace Codes Over F2 + uF2

被引：57
|
作者：
Shi, Minjia [1 ,2 ,3 ]
Liu, Yan [3 ]
Sole, Patrick [4 ]
机构：
[1] Anhui Univ, Key Lab Intelligent Comp & Signal Proc, Minist Educ, Hefei 230039, Peoples R China
[2] Southeast Univ, Natl Mobile Commun Res Lab, Nanjing 210096, Jiangsu, Peoples R China
[3] Anhui Univ, Sch Math Sci, Hefei 230601, Peoples R China
[4] Univ Paris 08, CNRS LAGA, F-93526 St Denis, France
来源：
IEEE COMMUNICATIONS LETTERS | 2016年 / 20卷 / 12期
关键词：
Two-weight codes; codes over rings; Griesmer bound; secret sharing schemes;
D O I：
10.1109/LCOMM.2016.2614934
中图分类号：
TN [电子技术、通信技术];
学科分类号：
0809 ;
摘要：
We construct an infinite family of two-Lee-weight codes over the ring F-2 + uF(2). These codes are defined as trace codes. They have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using character sums. By Gray mapping, we obtain an infinite family of abelian binary two-weight codes. They are shown to be optimal by application of the Griesmer bound. An application to secret sharing schemes is given.
引用
收藏
页码：2346 / 2349
页数：4
相关论文
共 50 条
  • [21] Macwilliams identities of linear codes over the ring F2 + uF2 + vF2
    Xiusheng Liu
    Hualu Liu
    Journal of Systems Science and Complexity, 2015, 28 : 691 - 701
  • [22] (F2 + uF2)(F4 + uF4)-Additive Cyclic Codes
    Lu, Jiyong
    IEEE ACCESS, 2022, 10 : 19112 - 19116
  • [23] Gray Map and Quantum Codes over the Ring F2 + uF2 + u2F2
    Yin, Xunru
    Ma, Wenping
    TRUSTCOM 2011: 2011 INTERNATIONAL JOINT CONFERENCE OF IEEE TRUSTCOM-11/IEEE ICESS-11/FCST-11, 2011, : 897 - 899
  • [24] A family of constacyclic codes over F2 + uF2 + vF2 + uvF2
    Xiaoshan Kai
    Shixin Zhu
    Liqi Wang
    Journal of Systems Science and Complexity, 2012, 25 : 1032 - 1040
  • [25] Upper bounds for the lengths of s-extremal codes over F2, F4, and F2 + uF2
    Han, Sunghyu
    Kim, Jon-Lark
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2008, 54 (01) : 418 - 422
  • [26] Constacyclic Codes of Length 2s Over Galois Extension Rings of F2 + uF2
    Dinh, Hai Q.
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2009, 55 (04) : 1730 - 1740
  • [27] (1 + uv)-cyclic codes over F2 + uF2 + vF2 + uvF2
    Yu, Hai-Feng
    Zhu, Shi-Xin
    Zhang, Xia
    Dianzi Yu Xinxi Xuebao/Journal of Electronics and Information Technology, 2014, 36 (06): : 1419 - 1422
  • [28] Self-dual codes over F2 + uF2 + vF2 + uvF2
    Yildiz, Bahattin
    Karadeniz, Suat
    JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2010, 347 (10): : 1888 - 1894
  • [29] Construction of extremal self-dual codes over F2 + uF2 with an automorphism of odd order
    Kim, Hyun Jin
    Lee, Yoonjin
    FINITE FIELDS AND THEIR APPLICATIONS, 2012, 18 (05) : 971 - 992
  • [30] New extremal binary self-dual codes of length 68 from quadratic residue codes over F2 + uF2 + u2F2
    Kaya, Abidin
    Yildiz, Bahattin
    Siap, Irfan
    FINITE FIELDS AND THEIR APPLICATIONS, 2014, 29 : 160 - 177
12345