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| Content Provider | IEEE Xplore Digital Library |
|---|---|
| Author | Bracken, C. Helleseth, T. |
| Copyright Year | 2009 |
| Description | Author affiliation: Department of Informatics, University of Bergen, PB 7803, N-5020, Norway (Helleseth, T.) || Department of Mathematics, National University of Maynooth, Logic House, South Campus, NUI, Co. Kildare, Ireland (Bracken, C.) |
| Abstract | The binary primitive triple-error-correcting BCH code is a cyclic code of minimum distance d = 7 with generator polynomial having zeros α, $α^{3}$ and $α^{5}$ where α is a primitive $(2^{n}$ − 1)-root of unity. The zero set of the code is said to be {1, 3, 5}. In the 1970's Kasami showed that one can construct similar triple-error-correcting codes using zero sets consisting of different triples than the BCH codes. Furthermore, in 2000 Chang et. al. found new triples leading to triple-error-correcting codes. In this paper a new such triple is presented. In addition a new method is presented that may be of interest in finding further such triples. The method is illustrated by giving a new and simpler proof of one of the known Kasami triples {1, $2^{k}$ + 1, $2^{3k}$ + 1} where n is odd and gcd(k, n) = 1 as well as to find the new triple given by {1, $2^{k}$ + 1, $2^{2k}$ + 1} for any n where gcd(k, n) = 1. |
| Starting Page | 1723 |
| Ending Page | 1725 |
| File Size | 521720 |
| Page Count | 3 |
| File Format | |
| ISBN | 9781424443123 |
| DOI | 10.1109/ISIT.2009.5205249 |
| Language | English |
| Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher Date | 2009-06-28 |
| Publisher Place | South Korea |
| Access Restriction | Subscribed |
| Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subject Keyword | Parity check codes Lead Galois fields Mathematics Logic Informatics Hamming distance Error correction codes Polynomials |
| Content Type | Text |
| Resource Type | Article |
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