Simplified High-Speed High-Distance List Decoding for Alternant Codes

This paper presents a simplified list-decoding algorithm to correct any number w of errors in any alternant code of any length n with any designed distance t+1 over any finite field Fq. The algorithm is efficient for w close to, and in many cases slightly beyond, the Fq Johnson bound J ′ = n′− √ n′(n′ − t− 1) where n′ = n(q−1)/q, assuming t+1 ≤ n′. In the typical case that qn/t ∈ (lgn) and that the parent field has (lgn) bits, the algorithm uses n(lgn) bit operations for w ≤ J ′ − n/(lgn); O(n) bit operations for w ≤ J ′ + o((lgn)/ lg lgn); and n bit operations for w ≤ J ′ + O((lgn)/ lg lgn).