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- W2591325174 abstract "In this chapter, self-dual and binary double-circulant codes based on primes are discussed. Many double-circulant codes are self-dual. Binary self-dual codes form an important class of codes due to their powerful error-correcting capabilities and their rich mathematical structure. This structure enables the entire weight distribution of a code to be determined. With these interesting properties, this family of codes has been a subject of extensive research for many years. For these codes that are longer than around 150 bits, an accurate determination of the codeword weight distributions has been an unsolved challenge. We show that the code structure may be used in a new algorithm that requires less codewords to be enumerated than traditional methods. We describe the new algorithm in detail and present new, complete, weight distribution results for codes of length 152, 168, 192, 194 and 200. We describe a modular congruence method and show how it can be used to check weight distributions of codes and have corrected some mistakes in previously published results for codes of length 137 and 151. For evaluation of the minimum Hamming distance for very long codes, a new probabilistic method has been presented along with results for codes up to 450 bits long. It is conjectured that the (136, 68, 24) self-dual code is the longest extremal code, meeting the upper bound for minimum Hamming distance, and that no other, longer, extremal code exists." @default.
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- W2591325174 date "2017-01-01" @default.
- W2591325174 modified "2023-09-25" @default.
- W2591325174 title "Algebraic Quasi Cyclic Codes" @default.
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- W2591325174 doi "https://doi.org/10.1007/978-3-319-51103-0_9" @default.
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