Classification of ?-Divisible Linear Codes Spanned by Codewords of Weight ?

IEEE TRANSACTIONS ON INFORMATION THEORY(2023)

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摘要
We classify all q-ary ?-divisible linear codes which are spanned by codewords of weight ?. The basic building blocks are the simplex codes, and for q = 2 additionally the first order Reed-Muller codes and the parity check codes. This generalizes a result of Pless and Sloane, where the binary self-orthogonal codes spanned by codewords of weight 4 have been classified, which is the case q = 2 and ? = 4 of our classification. As an application, we give an alternative proof of a theorem of Liu on binary ?-divisible codes of length 4? in the projective case.
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关键词
Codes, Linear codes, Generators, Binary codes, Systematics, Parity check codes, Reed-Muller codes, Linear code, divisible code, simplex code, Reed-Muller code, parity check code, self-orthogonal code
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