Erasure decoding of five times extended Reed-Solomon codes

Abstract

Recently a new family of error control codes was proposed which are equivalent to five times extended Reed-Solomon codes. In this paper an erasure decoding algorithm for these codes is proposed.

Decoding Five Times Extended Reed Solomon Codes Using Syndromes

“…• more than two errors in information symbol: In this case the complexity of procedures quantified by Υ 1I , Υ 2I , Υ 1P 1I can be added as the worst case: (16,6,23,9,2). (106)…”

“…In [1] it was shown that RS codes could be extended not only three times, but even five times when they are constructed over certain finite fields. For such five times extended RS codes a decoding algorithm is known [2] which is suitable only for erasure decoding. In case of erasures the positions are known in a received vector and therefore only the erasure values have to be found out during decoding.…”