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. https://resolver.caltech.edu/CaltechAUTHORS:20170927-074638028
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Abstract
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).
| Item Type: | Article | |||||||||
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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 | |||||||||
| DOI: | 10.1109/18.651000 | |||||||||
| Record Number: | CaltechAUTHORS:20170927-074638028 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170927-074638028 | |||||||||
| 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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=651000&isnumber=14195 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 81867 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 27 Sep 2017 16:24 | |||||||||
| Last Modified: | 15 Nov 2021 19:46 |
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