On codes correcting symmetric rank errors
NI Pilipchuk, EM Gabidulin - International Workshop on Coding and …, 2005 - Springer
NI Pilipchuk, EM Gabidulin
International Workshop on Coding and Cryptography, 2005•SpringerWe study the capability of rank codes to correct so-called symmetric errors beyond the
\left⌊d-12\right⌋ bound. If d≥n+12, then a code can correct symmetric errors up to the
maximal possible rank ⌊n-12⌋. If d≤n2, then the error capacity depends on relations
between d and n. If (d+j)\nmidn,\;j=0,1,\dots,m-1, for some m, but (d+ m)| n, then a code can
correct symmetric errors up to rank ⌊d+m-12⌋. In particular, one can choose codes
correcting symmetric errors up to rank d–1, ie, the error capacity for symmetric errors is about …
\left⌊d-12\right⌋ bound. If d≥n+12, then a code can correct symmetric errors up to the
maximal possible rank ⌊n-12⌋. If d≤n2, then the error capacity depends on relations
between d and n. If (d+j)\nmidn,\;j=0,1,\dots,m-1, for some m, but (d+ m)| n, then a code can
correct symmetric errors up to rank ⌊d+m-12⌋. In particular, one can choose codes
correcting symmetric errors up to rank d–1, ie, the error capacity for symmetric errors is about …
Abstract
We study the capability of rank codes to correct so-called symmetric errors beyond the bound. If , then a code can correct symmetric errors up to the maximal possible rank . If , then the error capacity depends on relations between d and n. If , for some m, but (d+m) | n, then a code can correct symmetric errors up to rank . 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.
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