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

被引：0
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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
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Keywords: Reed-Muller codes; Character sums.;
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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.
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页码：421 / 424
页数：3
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