An Elementary Proof to the Weight Distribution Formula of the First Order Shortened Reed-Muller Coset Code

被引：0

作者：

Hannu Tarnanen

机构：

[1] Department of Mathematics,

[2] University of Turku,undefined

[3] Fin-20014 Turku,undefined

[4] Finland,undefined

来源：

Applicable Algebra in Engineering, Communication and Computing | 1997年 / 8卷

关键词：

Keywords: Reed-Muller codes; Character sums.;

D O I：

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学科分类号：

摘要：

Let RM(m, r) be the shortened Reed-Muller code of order r and of length 2m−1. A simple proof to the Kasami’s weight distribution formula (see [2] and [3, p. 441]) of the cosets of RM(m, 1) in RM(m, 2) is given. The derivation of this distribution formula (21) is based only on elementary properties of the trace map and the Dickson theory of quadratic forms (see [1, pp. 197–199] and [3, pp. 434–442]) is no longer needed.

引用

页码：421 / 424

页数：3

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