MDS codes over F9 related to the ternary Golay code

A tower of geometries related to the ternary Golay codes

Yet another approach to the extended ternary Golay code

A new proof of the uniqueness and of the existence of the extended ternary Golay code is presented. The proof connects the code to the projective plane of order 3 and is of an elementary nature. The available proofs of the uniqueness of the extended ternary Golay code [2,7] are much more complicated than the standard corresponding proof in the binary case [2]. The prevailing opinion seems to be...

On the universal embedding of the near hexagon related to the extended ternary Golay code

Let E1 be the near hexagon on 729 points related to the extended ternary Golay code. We prove in an entirely geometricway that the generating and embedding ranks ofE1 are equal to 24. We also study the structure of the universal embeddinge of E1. More precisely, we consider several nice subgeometries A of E1 and determine which kind of embeddingeA is, whereeA is the embedding of A induced by...

Clay Codes: Moulding MDS Codes to Yield an MSR Code

With increase in scale, the number of node failures in a data center increases sharply. To ensure availability of data, failure-tolerance schemes such as ReedSolomon (RS) or more generally, Maximum Distance Separable (MDS) erasure codes are used. However, while MDS codes offer minimum storage overhead for a given amount of failure tolerance, they do not meet other practical needs of today’s dat...

Symbol-by-symbol APP decoding of the Golay code and iterative decoding of concatenated Golay codes

An efficient coset based symbol-by-symbol soft-in/soft-out APP decoding algorithm is presented for the Golay code. Its application in the iterative decoding of concatenated Golay codes is examined.