One Error and in the Given Interval Two Error Correcting Code for the Additive Communication Channel - Ghandilyan, Artur Kh.; Margaryan, Zhirayr G. (Mathematical Problems of Computer Science, 2021)
In this paper error correcting codes in the additive noisy communication channel are discussed. The system of boolean equalities are examined based on the Hamming parity check matrix. The metrical properties of the solutions of that system of equalities are examined based on Hamming distance. It is constructed a code based on the set of the solutions of above mentioned system of boolean equalities and it is proved that the constructed code is correcting any single error and any two errors which occur in the given interval.