TRIPLE CIRCULANT CODES BASED ON QUADRATIC RESIDUES

• 발행기관: 충청수학회
• 저자명: Sung hyu Han
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 23, No. 1, 91~98쪽, 전체 8쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2010.03.30

영문 초록

One of the most interesting classes of algebraic codes is the class of quadratic residue (QR) codes over a finite field. A natural construction doubling the lengths of QR codes seems to be the double circulant constructions based on quadratic residues given by Karlin, Pless, Gaborit, et. al. In this paper we define a class of triple circulant linear codes based on quadratic residues. We construct many new optimal codes or codes with the highest known parameters using this construction. In particular, we find the first example of a ternary [58, 20, 20] code, which improves the previously known highest minimum distance of any ternary [58, 20] codes.

목차

1. Introduction

2. Preliminaries

3. Square root bound and automorphism group

4. Construction results

Acknowledgments

References