Efficient indexing of necklaces and irreducible polynomials over finite fields

Swastik Kopparty, Mrinal Kumar, Michael Saks

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations

Abstract

We study the problem of indexing necklaces, and give the first polynomial time algorithm for this problem. Specifically, we give a poly(n, log|∑|)-time computable bijection between {1,...,|N|} and the set N of all necklaces of length n over a finite alphabet ∑. Our main application is to give an explicit indexing of all irreducible polynomials of degree n over the finite field double-struck Fq in time poly(n, logq) (with n logq bits of advice). This has applications in pseudorandomness, and answers an open question of Alon, Goldreich, Håstad and Peralta [2].

Original languageEnglish (US)
Title of host publicationAutomata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Proceedings
PublisherSpringer Verlag
Pages726-737
Number of pages12
EditionPART 1
ISBN (Print)9783662439470
DOIs
StatePublished - 2014
Event41st International Colloquium on Automata, Languages, and Programming, ICALP 2014 - Copenhagen, Denmark
Duration: Jul 8 2014Jul 11 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume8572 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other41st International Colloquium on Automata, Languages, and Programming, ICALP 2014
Country/TerritoryDenmark
CityCopenhagen
Period7/8/147/11/14

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science

Fingerprint

Dive into the research topics of 'Efficient indexing of necklaces and irreducible polynomials over finite fields'. Together they form a unique fingerprint.

Cite this