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A construction of $ \mathbb{F}_2 $-linear cyclic, MDS codes
2019
Advances in Mathematics of Communications
In this paper we construct F 2 -linear codes over F b 2 with length n and dimension n − r where n = rb. These codes have good properties, namely cyclicity, low density parity-check matrices and maximum distance separation in some cases. For the construction, we consider an odd prime p, let n = p − 1 and utilize a partition of Zn. Then we apply a Zech logarithm to the elements of these sets and use the results to construct an index array which represents the parity-check matrix of the code.
doi:10.3934/amc.2020047
fatcat:wxpeusoiurbgherekheykualwy