Titlebook: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes; 17th International S Serdar Boztaş,Hsiao-Feng (Francis) Lu Conference pro

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Generalized Sudan’s List Decoding for Order Domain CodesWe generalize Sudan’s list decoding algorithm without multiplicity to evaluation codes coming from arbitrary order domains. The number of correctable errors by the proposed method is larger than the original list decoding without multiplicity.

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Space-Time Codes from Crossed Product Algebras of Degree 4We study crossed product algebras of degree 4, and present a new space-time code construction based on a particular crossed product division algebra which exhibits very good performance.

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Correctable Errors of Weight Half the Minimum Distance Plus One for the First-Order Reed-Muller Codea cryptographic viewpoint, this result immediately leads to the exact number of Boolean functions of . variables with nonlinearity 2. + 1. The notion of . and ., which is introduced by Helleseth, Kløve, and Levenshtein to describe the monotone structure of correctable/uncorrectable errors, plays a significant role in the result.

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