A class of optimal linear codes of length one above the Griesmer bound |
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Authors: | E. J. Cheon |
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Affiliation: | (1) Department of Mathematics and RINS, Gyeongsang National University, Jinju, 660-701, Korea |
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Abstract: | In this paper, we determine the smallest lengths of linear codes with some minimum distances. We construct a [g q (k, d) + 1, k, d] q code for sq k-1 − sq k-2 − q s − q 2 + 1 ≤ d ≤ sq k-1 − sq k-2 − q s with 3 ≤ s ≤ k − 2 and q ≥ s + 1. Then we get n q (k, d) = g q (k, d) + 1 for (k − 2)q k-1 − (k − 1)q k-2 − q 2 + 1 ≤ d ≤ (k − 2)q k-1 − (k − 1)q k-2, k ≥ 6, q ≥ 2k − 3; and sq k-1 − sq k-2 − q s − q + 1 ≤ d ≤ sq k-1 − sq k-2 − q s , s ≥ 2, k ≥ 2s + 1 and q ≥ 2s − 1. This work was partially supported by the Com2MaC-SRC/ERC program of MOST/KOSEF (grant # R11-1999-054) and was partially supported by the Korea Research Foundation Grant funded by the Korean Government(MOEHRD)(KRF-2005-214-C00175). |
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Keywords: | Griesmer bound Linear code 0-cycle Minimum length Minihyper Projective space |
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