Some best rate 1/p and rate (p-1)/p systematic quasi-cyclic codes over GF(3) and GF(4)

Author

Gulliver, T. Aaron ; Bhargava, Vijay K.

Author_Institution

Dept. of Syst. & Comput. Eng., Carleton Univ., Ottawa, Ont., Canada

Volume

38

Issue

4

fYear

1992

fDate

7/1/1992 12:00:00 AM

Firstpage

1369

Lastpage

1374

Abstract

The class of quasi-cyclic (QC) codes has been proven to contain many good codes. To date the known QC codes are primarily rate 1/p and (p-1)/p binary codes constructed from circulant matrices. These results are extended to QC codes over GF(3) and GF(4). Codes are constructed using integer linear programming and heuristic combinatorial optimization. Many of these attain the maximum possible minimum distance for any linear code with the same parameters, and several improve the maximum known distances. The link between power residue (PR) codes and QC codes is exploited as a means of constructing new QC codes and to initialize the search algorithm. Previously unknown minimum distances for nonbinary quadratic residue codes are given. The minimum distances for the PR codes and the maximum known distances for the QC codes are tabulated

Keywords

error correction codes; integer programming; linear programming; optimisation; GF(3); GF(4); heuristic combinatorial optimization; integer linear programming; linear code; maximum known distances; minimum distance; nonbinary quadratic residue codes; power residue codes; rate (p-1)/p binary codes; rate 1/p binary codes; search algorithm; systematic quasi-cyclic codes; Binary codes; Block codes; Cities and towns; Convolutional codes; Councils; Hamming distance; Integer linear programming; Linear code; Reed-Solomon codes; Systems engineering and theory;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.144719

Filename

144719