Construction of Systematic Binary Self-Complementary Codes




Medda, Jonaki

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Efficient transmission of data through channels is of utmost importance in modern digital communication systems. In order to reduce errors due to impairments such as noise in the channel, error control coding is used for reliable transmission of data. This work is focused on a class of linear block codes called binary self-complementary codes which contain the all-ones codeword. The construction of binary self-complementary codes and their weight distributions are considered. The Magma Computational Algebra System is used to generate the weight distributions of the best codes in terms of the minimum Hamming distance. General expressions for the Hamming weight distributions of the best codes for small dimensions are obtained and the best self-complementary codes are compared with the best possible linear codes based on the minimum Hamming distance. The results indicate that the best self-complementary codes have minimum distances which are similar to those of the best binary linear codes with differences of 1, 2 and 3 for 34, 7 and 1 values of n, respectively, for n ≤ 16.



self-complementary, Error Control Coding, Magma