Constructing rate 1/p systematic binary quasi-cyclic codes based on the matroid theory

Authors:
Guangfu Wu;Hsin-Chiu Chang;Lin Wang;T. K. Truong
Affiliations:
Department of Communication Engineering, College of Information Science and Technology, Xiamen University, Xiamen, China 361005;Department of Information Engineering, I-Shou University, Kaohsiung, Taiwan;Department of Communication Engineering, College of Information Science and Technology, Xiamen University, Xiamen, China 361005;Department of Information Engineering, I-Shou University, Kaohsiung, Taiwan and Department of Computer Science and Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan
Venue:
Designs, Codes and Cryptography
Year:
2014

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Abstract

In this paper, rate 1/p binary systematic quasi-cyclic (QC) codes are constructed based on Matroid Theory (MT). The relationship between the generator matrix and minimum distance d is derived through MT, which is benefit to find numbers of QC codes with large minimum distance by our Matroid search algorithm. More than seventy of QC codes that extend previously published results are presented. Among these codes, there are nine codes whose minimum distance is larger than those of the known codes found by Gulliver et al.