On codes correcting symmetric rank errors

Abstract

We study the capability of rank codes to correct so-called symmetric errors beyond the [d-1/2] bound. If d ≥ n+1/2, then a code can correct symmetric errors up to the maximal possible rank [n-1/2]. If d ≤ n/2, then the error capacity depends on relations between d and n. If (d + j) n, j = 0, 1,..., m - 1, for some m, but (d + m) , then a code can correct symmetric errors up to rank [d+m-1/2]. In particular, one can choose codes correcting symmetric errors up to rank d - 1, i.e., the error capacity for symmetric errors is about twice more than for general errors. © Springer-Verlag Berlin Heidelberg 2006.