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Two remarks on a paper by Moreno and Kumar [binary Reed-Muller codes]

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1 Author(s)
J. Lahtonen ; Dept. of Math., Turku Univ., Finland

O. Moreno and P.V. Kumar (IEEE Trans. Inform. Theory, vol.39, no.5, September 1993) showed how Deligne's theorem can be applied to coding theory. They studied certain subcodes of binary Reed-Muller codes and estimated the associated character sums over a field of q2 elements. They obtained bounds of the order 𝒪(q). The present paper shows that in one case one can improve the coefficient of q in the estimates. The author also shows that there is an error in Moreno and Kumar's argument and in some cases one needs need to replace a bound of the order 𝒪(q) by a weaker bound of the order 𝒪(q 3/2)

Published in:

IEEE Transactions on Information Theory  (Volume:41 ,  Issue: 3 )