Binary Self-Complementary Codes

Abstract

A binary linear code C is said to be self-complementary if the all-ones codeword belongs to C. This report focuses on binary self-complementary codes and their weight distributions which in some cases are generated using the MAGMA Computational Algebra System. Several classes of binary codes, namely Hamming, simplex, single parity check, repetition, extended Hamming and Reed-Muller, are examined. This report considers binary codes up to length 12, and the best self-complementary codes are compared to the best linear codes. Future research can consider binary codes of longer lengths and nonbinary codes.