New Good Rate (m-1)/pm Ternary and Quaternary Quasi-Cyclic Codes

Authors:
T. Aaron Gulliver;Vijay K. Bhargava
Affiliations:
Department of Systems and Computer Engineering, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, Canada K1S 5B6 gulliver@sce.carleton.ca;Department of Electrical and Computer Engineering, University of Victoria, P.O. Box 3055, MS 8610, Victoria, B. C., Canada V8W 3P6 bhargava@sirius.uvic.ca
Venue:
Designs, Codes and Cryptography
Year:
1996

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Abstract

Previous results have shown that the class of quasi-cyclic (QC) codes contains many good codes. In this paper, new rate (m - 1)/pm QC codes over GF(3) and GF(4) are presented. These codes have been constructed using integer linear programming and a heuristic combinatorial optimization algorithm based on a greedy local search. Most of these codes attain the maximum possible minimum distance for any linear code with the same parameters, i.e., they are optimal, and 58 improve the maximum known distances. The generator polynomials for these 58 codes are tabulated, and the minimum distances of rate (m - 1)/pm QC codes are given.