List decoding of crisscross error patterns

Abstract

List decoding of crisscross errors in arrays over finite fields is considered. A Johnson-like upper bound on the maximum list size in the cover metric is derived, showing that the list of codewords has polynomial size up to a certain radius. Further, a simple list decoding algorithm for a known optimal code construction is presented, which decodes errors in the cover metric up to our upper bound. These results reveal significant differences between the cover metric and the rank metric.

Construction of new codes in term‐rank metric

“…In coding theory, this norm appeared in [10,11]. See also [12][13][14][15][16][17][18]. The function ρ(A) satisfies all the axioms of the norm [19]: The distance between two matrices A 1 and A 2 is the term-rank of their difference:…”