DETERMINATION OF MINIMUM LENGTH OF SOME LINEAR CODES

• 발행기관: 충청수학회
• 저자명: Eun Ju Cheon
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 26, No. 1, 147~159쪽, 전체 13쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2013.02.28

영문 초록

Hamada ([8]) and Maruta ([17]) proved the minimum length n3(6; d) = g3(6; d) + 1 for some ternary codes. In this paper we consider such minimum length problem for q ¸ 4, and we prove that nq(6; d) = gq(6; d)+1 for d = q5 ¡q3 ¡q2 ¡2q +e, 1 · e · q. Combining this result with Theorem A in [4], we have nq(6; d) =gq(6; d) + 1 for q5 ¡ q3 ¡ q2 ¡ 2q + 1 · d · q5- ¡ q3- ¡ q2 -with q ¸ 4.Note that nq(6; d) = gq(6; d) for q5 -¡ q3- ¡ q2 + 1 · d · q5 by Theorem 1.2.

목차

1. Introduction

2. Preliminaries

3. Main theorem