DETERMINATION OF MINIMUM LENGTH OF SOME LINEAR CODES

Abstract

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.

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