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Shadow bounds for self-dual codes

Rains, Eric M. (1998) Shadow bounds for self-dual codes. IEEE Transactions on Information Theory, 44 (1). pp. 134-139. ISSN 0018-9448. doi:10.1109/18.651000.

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Conway and Sloane (1990) have previously given an upper bound on the minimum distance of a singly-even self-dual binary code, using the concept of the shadow of a self-dual code. We improve their bound, finding that the minimum distance of a self-dual binary code of length n is at most 4[n/24]+4, except when n mod 24=22, when the bound is 4[n/24]+6. We also show that a code of length a multiple of 24 meeting the bound cannot be singly-even. The same technique gives similar results for additive codes over GF(4) (relevant to quantum coding theory).

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Additional Information:© 1998 IEEE. Manuscript received January 21, 1997; revised June 20, 1997. The author wishes to thank N. Sloane for many productive conversations; in particular, for introducing the author to shadow theory.
Subject Keywords:Bound, self-dual code, shadow, singly-even
Issue or Number:1
Record Number:CaltechAUTHORS:20170927-074638028
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Official Citation:E. M. Rains, "Shadow bounds for self-dual codes," in IEEE Transactions on Information Theory, vol. 44, no. 1, pp. 134-139, Jan 1998. doi: 10.1109/18.651000 URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81867
Deposited By: Tony Diaz
Deposited On:27 Sep 2017 16:24
Last Modified:15 Nov 2021 19:46

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