New linear codes from constacyclic codes

作     者：Aydin, Nuh Murphree, John M. 

作者机构：Kenyon Coll Dept Math Gambier OH 43022 USA 

出 版 物：《JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS》 (佛兰克林学会杂志)

年 卷 期：2014年第351卷第3期

页      面：1691-1699页

核心收录：

学科分类：0808[工学-电气工程] 07[理学] 08[工学] 0701[理学-数学] 0811[工学-控制科学与工程] 

主　　题：LINEAR codes CODING theory COMBINATORIAL analysis PARAMETER estimation SEARCH algorithms COMPUTATIONAL complexity 

摘      要：One of the main challenges of coding theory is to construct linear codes with the best possible parameters. Various algebraic and combinatorial methods along with computer searches are used to construct codes with better parameters. Given the computational complexity of determining the minimum distance of a code, exhaustive searches are not feasible for all but small parameter sets. Therefore, codes with certain algebraic structures are preferred for both theoretical and practical reasons. In this work we focus on the class of constacyclic codes to first generate all constacyclic codes exhaustively over small finite fields of order up to 9 to create a database of best constacyclic codes. We will then use this database as a building block for a search algorithm for new quasi-twisted codes. Our search on constacyclic codes has revealed 16 new codes, i.e. codes with better parameters than currently best-known linear codes. Given that constacyclic codes are well known, this is a surprising result. Moreover, using the standard constructions of puncturing, shortening or extending a given code, we also derived 55 additional new codes from these constacyclic codes. Hence, we achieved improvements on 71 entries in the database of best-known codes. We use a search strategy that is comprehensive, i.e. it computes every constacyclic code for a given length and shift constant, and it avoids redundantly examining constacyclic codes that are equivalent to either cyclic codes or other constacyclic codes. (C) 2013 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.