Construction of some binary linear codes of minimum distance five

A method of constructing binary linear codes that have a minimum Hamming distance of five is presented. The author proposes a general formulation of the parity check matrix for the desired code and then derives necessary conditions for the code to have a minimum distance of five. Some new codes that satisfy the necessary conditions are described. Some efficient new codes are obtained. In particular, a (47,36,5) code is obtained that has six more information bits than the best previously known code with 11 check bits.<
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