Alternant code
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In coding theory, alternant codes form a class of parameterised error-correcting codes which generalise the BCH codes.
In coding theory, alternant codes form a class of parameterised error-correcting codes which generalise the BCH codes. ==Definition== An alternant code over GF(q) of length n is defined by a parity check matrix H of alternant form H i,j = α j i y i , where the α j are distinct elements of the extension GF(q m ), the y i are further non-zero parameters again in the extension GF(q m ) and the indices range as i from 0 to δ − 1, j from 1 to n. ==Properties== The 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 BCH codes Goppa codes Srivastava codes
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