Pless, Vera (1986) Q-codes. Journal of Combinatorial Theory. Series A, 43 (2). pp. 258-276. ISSN 0097-3165. doi:10.1016/0097-3165(86)90066-X. https://resolver.caltech.edu/CaltechAUTHORS:20180720-163624108
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Abstract
We introduce a new infinite family of quaternary cyclic (n,(n+1)2) and (n,(n − 1)2) codes which include Q. R. codes when n is prime. These codes are defined in terms of their idempotent generators and exist for all odd n. Every self-dual (s.d.) or strictly self-dual (s.s.d.) extended cyclic code is an extended Q-code. As for Q. R. codes, there is a square root bound on the odd-like minimum weight. We can tell by the factors of n whether s.d. or s.s.d. extended cyclic codes exist and when all or some extended Q-codes are s.d. or s.s.d. We know when Q-codes have binary idempotents and when the binary subcode is just the all-one vector. A table of Q-codes of modest lengths is given. Minimum weights, idempotents and duals are identified.
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| Additional Information: | © 1986 Published by Elsevier. Received 28 March 1986. This work was supported in part by the National Science Foundation Grants MCS-8201311, R11-8503096 and NSA Grant MDA 904-85-H-0016. I wish to acknowledge very helpful conversations with Dr. John Masley. In particular, he proved major portions of Theorems 8, 10, and Corollary 2 of Theorem 11. I wish to thank Professor Richard Wilson for pointing out that Theorem 20 is part of Mann's theorem and for other helpful comments. I wish to thank Professor Noburu Ito for many helpful comments and for a careful reading of this paper leading to several corrections. The minimum weights, weight distributions, and groups of the codes in Tables I and II were computed by the CAMAC system [2] running on the University of Illinois at Chicago computer. | ||||||||
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| Issue or Number: | 2 | ||||||||
| DOI: | 10.1016/0097-3165(86)90066-X | ||||||||
| Record Number: | CaltechAUTHORS:20180720-163624108 | ||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20180720-163624108 | ||||||||
| Official Citation: | Vera Pless, Q-codes, Journal of Combinatorial Theory, Series A, Volume 43, Issue 2, 1986, Pages 258-276, ISSN 0097-3165, https://doi.org/10.1016/0097-3165(86)90066-X. (http://www.sciencedirect.com/science/article/pii/009731658690066X) | ||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||
| ID Code: | 88110 | ||||||||
| Collection: | CaltechAUTHORS | ||||||||
| Deposited By: | George Porter | ||||||||
| Deposited On: | 23 Jul 2018 22:33 | ||||||||
| Last Modified: | 16 Nov 2021 00:24 |
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