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Maximum Distance Separable Codes
A Course in Algebraic Error-Correcting Codes, 2020Two codewords of a block code of length n and minimum distance d must differ on any set of n − d + 1 coordinates, since they are at distance at least d from each other. This observation leads to the Singleton bound, Theorem 6.1. A code whose parameters give an equality in the Singleton bound is called a maximum distance separable code or simply an MDS ...
Simeon Ball
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Maximum Distance Separable Array Codes Allowing Partial Collaboration
IEEE Communications Letters, 2020This letter considers the problem of repairing multiple node failures through partial collaboration in a distributed storage system (DSS). In the repair process, each failed node firstly connects to $d\geq k$ alive nodes to download data, and then ...
Yuejia Zhang, Shiqiu Liu, Li Chen
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Pseudocyclic maximum- distance-separable codes
IEEE Transactions on Information Theory, 1990The (n, k) pseudocyclic maximum-distance-separable (MDS) codes modulo (x/sup n/-a) over GF(q) are considered. Suppose that n is a divisor of q+1. If n is odd, pseudocyclic MDS codes exist for all k. However, if n is even, nontrivial pseudocyclic MDS codes exist for odd k (but not for even k) if a is a quadratic residue in GF(q), and they exist for even
A. Krishna, D. Sarwate
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Short Nonbinary Maximum Distance Separable Cycle Codes
IEEE Communications Letters, 2018This letter presents a class of very short nonbinary cycle codes that are maximum distance separable (MDS). It is proved that there is one and only one regular graph on which MDS cycle codes may be constructed and only for finite field orders larger than or equal to 5.
B. Matuz, G. Liva, E. Paolini
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