Five Times Extended Reed-Solomon Codes Applicable in Memory Storage Systems

Erasure decoding of five times extended Reed-Solomon codes

“…In this paper a decoding algorithm was presented for the recently discovered codes described in [5]. This algorithm allows correcting up to 4 erasures in each codeword of these codes.…”

“…For example, the corresponding symbols can be lost during the transmission or the detector can delete the least reliable symbols and give the decoder the additional information of which symbols were deleted. Since the code distance of the analyzed codes d m = 5 , the new codes from [5] can correct up to 4 erasures in one codeword or, mathematically expressed, z = 4 . In this section we will describe one method of correcting 4 symbol erasures.…”

“…Recently in [5] a new family of error control codes constructed over GF (q) was proposed, where q = 2 m and m is an odd integer, using control matrix…”

“…This infinite family of codes can be characterized by the following triple [n = q + 4, q − 1, 5]. In [5] the construction of these codes together with the proof that each code from this family has d m = 5 was presented. In [5] no decoding method was described.…”

“…In [5] the construction of these codes together with the proof that each code from this family has d m = 5 was presented. In [5] no decoding method was described. However, to make these codes useful in practice, knowing an implementable decoding method is necessary.…”