A refinement of Cusick-Cheon bound for the second order binary Reed-Muller code

Thomas W. Cusick; Yuri L. Borissov

doi:10.1016/j.disc.2010.08.016

A refinement of Cusick-Cheon bound for the second order binary Reed-Muller code

Thomas W. Cusick
, Yuri L. Borissov

Mathematics

Bulgarian Academy of Sciences

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We prove a stronger form of the conjectured CusickCheon lower bound for the number of quadratic balanced Boolean functions. We also prove various asymptotic results involving B(k,m), the number of balanced Boolean functions of degree ≤k in m variables, in the case k=2. Finally, we connect our results for k=2 with the (still unproved) conjectures of CusickCheon for the functions B(k,m) with k>2.

Original language	English
Pages (from-to)	3537-3543
Number of pages	7
Journal	Discrete Mathematics
Volume	310
Issue number	24
DOIs	https://doi.org/10.1016/j.disc.2010.08.016
State	Published - Dec 28 2010

Keywords

Asymptotics
Balanced
Boolean function
ReedMuller code

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10.1016/j.disc.2010.08.016

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N2 - We prove a stronger form of the conjectured CusickCheon lower bound for the number of quadratic balanced Boolean functions. We also prove various asymptotic results involving B(k,m), the number of balanced Boolean functions of degree ≤k in m variables, in the case k=2. Finally, we connect our results for k=2 with the (still unproved) conjectures of CusickCheon for the functions B(k,m) with k>2.

AB - We prove a stronger form of the conjectured CusickCheon lower bound for the number of quadratic balanced Boolean functions. We also prove various asymptotic results involving B(k,m), the number of balanced Boolean functions of degree ≤k in m variables, in the case k=2. Finally, we connect our results for k=2 with the (still unproved) conjectures of CusickCheon for the functions B(k,m) with k>2.

KW - Asymptotics

KW - Balanced

KW - Boolean function

KW - ReedMuller code

UR - https://www.scopus.com/pages/publications/77958008747

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DO - 10.1016/j.disc.2010.08.016

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JO - Discrete Mathematics

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IS - 24

ER -

A refinement of Cusick-Cheon bound for the second order binary Reed-Muller code

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Keywords

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