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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: September 25, 1996; revised version: March 11, 1997
Rights and permissions
About this article
Cite this article
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
Issue Date:
DOI: https://doi.org/10.1007/s002000050081