NDLI: On the Fast Computation of the Weight Enumerator Polynomial and the $t$ Value of Digital Nets over Finite Abelian Groups

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Matsumoto, Makoto Dick, Josef
Copyright Year	2013
Abstract	In this paper we introduce digital nets over finite abelian groups which contain digital nets over finite fields and certain rings as a special case. We prove a MacWilliams-type identity for such digital nets. This identity can be used to compute the strict $t$-value of a digital net over finite abelian groups. If the digital net has $N$ points in the $s$-dimensional unit cube $[0,1)^s$, then the $t$-value can be computed in $\mathcal{O}(N s \log N)$ operations and the weight enumerator polynomial can be computed in $\mathcal{O}(N s (\log N)^2)$ operations, where operations mean arithmetic of integers. By precomputing some values the number of operations of computing the weight enumerator polynomial can be reduced further.
Starting Page	1335
Ending Page	1359
Page Count	25
File Format	PDF
ISSN	08954801
DOI	10.1137/120893677
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	3
Volume Number	27
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2013-08-06
Access Restriction	Subscribed
Subject Keyword	digital net weight enumerator polynomial Numerical integration Irregularities of distribution, discrepancy Pseudo-random numbers; Monte Carlo methods quasi--Monte Carlo MacWilliams identity finite abelian group Algebraic coding theory; cryptography Linear codes, general Discrete and fast Fourier transforms
Content Type	Text
Resource Type	Article
Subject	Mathematics

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