Alternant code
In coding theory, alternant codes form a class of parameterised error-correcting codes which generalise the BCH codes.
Definition
An alternant code over GF of length n is defined by a parity check matrix H of alternant form Hi,''j = αjiy''i, where the αj are distinct elements of the extension GF, the yi are further non-zero parameters again in the extension GF 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