Coset Analysis of Reed Muller Codes Via Translates of Finite Vector Spaces
نویسندگان
چکیده
In order to calculate the error probability of a code it is necessary to know the distribution of the coset leaders. The enumeration of cosets of the first order Reed Muller code has been studied (i) by Berlekamp and Welch (1972) by associating with each coset a class of Boolean functions, and (ii) by Sloane and Dick (1971) by associating with each coset a class of single-error-correcting codes called structure codes. It is shown here that it is possible to have two vectors of the same weight and in the same coset, which yet have inequivalent structure codes, at least for lengths /> 128, thus giving a negative answer to a question raised by Sloane and Dick.
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ورودعنوان ژورنال:
- Information and Control
دوره 20 شماره
صفحات -
تاریخ انتشار 1972