On list decoding of alternant codes in the hamming and lee metrics
Ido Tal, Ron M. Roth · 2003
Fix some metric d : F × F → R. A list-l decoder for Calt (with respect to d(·, ·)) can now be designed as follows. Find an integer β and a mapping M : F → N such that for the largest possible integer τ , the following two conditions hold for the matrix M(y) that corresponds to any received word y, whenever a codeword c ∈ Calt satisfies d(c,y) ≤ τ : (C1) SM(y)(c) ≥ β. (C2) (i) and (ii) are satisfied by some Q(x, z) 6= 0.