Abstract.
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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Received: September 25, 1996; revised version: March 11, 1997
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Tarnanen, H. An Elementary Proof to the Weight Distribution Formula of the First Order Shortened Reed-Muller Coset Code. AAECC 8, 421–424 (1997). https://doi.org/10.1007/s002000050081
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DOI: https://doi.org/10.1007/s002000050081