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• W2949659323 abstract "Revisiting an approach by Conway and Sloane we investigate a collection of optimal non-linear binary codes and represent them as (non-linear) codes over Z4. The Fourier transform will be used in order to analyze these codes, which leads to a new algebraic representation involving subgroups of the group of units in a certain ring. One of our results is a new representation of Best's (10, 40, 4) code as a coset of a subgroup in the group of invertible elements of the group ring Z4[Z5]. This yields a particularly simple algebraic decoding algorithm for this code. The technique at hand is further applied to analyze Julin's (12, 144, 4) code and the (12, 24, 12) Hadamard code. It can also be used in order to construct a (non-optimal) binary (14, 56, 6) code." @default.
• W2949659323 created "2019-06-27" @default.
• W2949659323 creator A5019886277 @default.
• W2949659323 creator A5056687416 @default.
• W2949659323 date "2011-09-22" @default.
• W2949659323 modified "2023-09-27" @default.
• W2949659323 title "On the algebraic representation of selected optimal non-linear binary codes" @default.
• W2949659323 cites W2000874261 @default.
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• W2949659323 hasPublicationYear "2011" @default.
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