| 词条 | Alternant code |
| 释义 |
In coding theory, alternant codes form a class of parameterised error-correcting codes which generalise the BCH codes. DefinitionAn alternant code over GF(q) of length n is defined by a parity check matrix H of alternant form Hi,j = αjiyi, where the αj are distinct elements of the extension GF(qm), the yi are further non-zero parameters again in the extension GF(qm) and the indices range as i from 0 to δ − 1, j from 1 to n. PropertiesThe parameters of this alternant code are length n, dimension ≥ n − mδ and minimum distance ≥ δ + 1. There exist long alternant codes which meet the Gilbert-Varshamov bound. The class of alternant codes includes
References
3 : Error detection and correction|Finite fields|Coding theory |
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