The nonexistence of near-extremal formally self-dual codes |
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Authors: | Sunghyu Han Jon-Lark Kim |
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Affiliation: | (1) Department of Mathematics, Institute of Mathematical Sciences, Ewha Womans University, Seoul, 120-750, South Korea;(2) Department of Mathematics, University of Louisville, Louisville, KY 40292, USA |
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Abstract: | A code is called formally self-dual if and have the same weight enumerators. There are four types of nontrivial divisible formally self-dual codes over , and . These codes are called extremal if their minimum distances achieve the Mallows-Sloane bound. S. Zhang gave possible lengths for which extremal self-dual codes do not exist. In this paper, we define near-extremal formally self-dual (f.s.d.) codes. With Zhang’s systematic approach, we determine possible lengths for which the four types of near-extremal formally self-dual codes as well as the two types of near-extremal formally self-dual additive codes cannot exist. In particular, our result on the nonexistence of near-extremal binary f.s.d. even codes of any even length n completes all the cases since only the case 8|n was dealt with by Han and Lee. |
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Keywords: | Extremal codes Formally self-dual codes Near-extremal codes Self-dual codes |
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