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2019•Letters of the IEEE Computer SocietyRequires access

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

Martin Rakús, Peter Farkaš, Tomáš Páleník, Andrej Danis

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Abstract

In this letter it is proved that five times extended Reed-Solomon codes contain an infinite subset of almost MDS codes with parameters: [(q - 1) + 5, (q - 1), 5]GF(2m)which are defined over a finite field GF(2m) where m ≥ 3 is a positive odd integer. The first three of these codes reach an upper bound for linear block code distance for the corresponding codeword lengths and number of information symbols in codewords in existing tables for optimal code parameters [1]. The relevant parts of weight spectra for the first four codes confirm the code parameters.

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In this letter it is proved that five times extended Reed-Solomon codes contain an infinite subset of almost MDS codes with parameters: [(q - 1) + 5, (q - 1), 5]GF(2m)which are defined over a finite field GF(2m) where m ≥ 3 is a positive odd integer. The first three of these codes reach an upper bound for linear block code distance for the corresponding codeword lengths and number of information symbols in codewords in existing tables for optimal code parameters [1]. The relevant parts of weight spectra for the first four codes confirm the code parameters.

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Available abstract

In this letter it is proved that five times extended Reed-Solomon codes contain an infinite subset of almost MDS codes with parameters: [(q - 1) + 5, (q - 1), 5]GF(2m)which are defined over a finite field GF(2m) where m ≥ 3 is a positive odd integer. The first three of these codes reach an upper bound for linear block code distance for the corresponding codeword lengths and number of information symbols in codewords in existing tables for optimal code parameters [1]. The relevant parts of weight spectra for the first four codes confirm the code parameters.

Key concepts: Code word, Reed–Solomon error correction, Code (set theory), Finite field, Integer (computer science), Discrete mathematics, Combinatorics, Block (permutation group theory)

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