A Method to Enlarge the Design Distance of BCH Codes and Some Classes of Infinite Optimal Cyclic Codes

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10726)

Abstract

Cyclic codes are a meaningful class of linearcodes due to their effective encoding and decoding algorithms. As a subclass of cyclic codes, Bose-Ray-Chaudhuri-Hocquenghem (BCH) codes have good error-correcting capability and are widely used in communication systems. As far as the design of cyclic codes is concerned, it is difficult to determine the minimum distance. It is well known that the minimum distance of a cyclic code of designed distance d is at least d. In this paper, by adjusting the generator polynomial slightly and using a concatenation technique, we present a method to enlarge the designed distance of cyclic codes and obtain two classes of \([pq,q-1,2p]\) cyclic codes and \([pq,p-1,2q]\) cyclic codes over GF(2). As a consequence, a class of infinite optimal [3p, 2, 2p] cyclic codes, where \(p\equiv {-1}\pmod 8\), with respect to the Plotkin bound over GF(2) is presented.

Keywords

Cyclic code Cyclotomic sequence Finite fields 

Notes

Acknowledgment

This work was partially supported by the National Natural Science Foundation of China (Grant No. 11771007, 11601177 and 61572027). The first author was also supported by the Funding of Jiangsu Innovation Program for Graduate Education (Grant No. KYZZ15_0090), the Funding for Outstanding Doctoral Dissertation in NUAA (Grant No. BCXJ16-08), the Open Project Program of Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University (Grant No. GDSXJCKX2016-07) and the Funding of Nanjing Institute of Technology (Grant No. CKJB201606).

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsNanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.Department of Mathematics and PhysicsNanjing Institute of TechnologyNanjingChina
  3. 3.Key Laboratory of Mathematics and Interdisciplinary Sciences, Guangdong Higher Education InstitutesGuangzhou UniversityGuangzhouChina

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