Cyclic Sieving for cyclic codes

Alex Mason, Victor Reiner, Shruthi Sridhar

Research output: Contribution to journalArticlepeer-review

Abstract

Prompted by a question of Jim Propp, this paper examines the cyclic sieving phenomenon (CSP) in certain cyclic codes. For example, it is shown that, among dual Hamming codes over Fq, the generating function for codedwords according to the major index statistic (resp. the inversion statistic) gives rise to a CSP when q=2 or q=3 (resp. when q=2). A byproduct is a curious characterization of the irreducible polynomials in F2[x] and F3[x] that are primitive.

Original languageEnglish (US)
Article number101846
JournalFinite Fields and their Applications
Volume73
DOIs
StatePublished - Aug 2021

Bibliographical note

Funding Information:
This research was carried out as part of the 2017 REU program at the School of Mathematics at University of Minnesota, Twin Cities. The authors are grateful for the support of National Science Foundation RTG grant DMS-1148634 .

Publisher Copyright:
© 2021 Elsevier Inc.

Keywords

  • Cyclic codes
  • Cyclic sieving
  • Descent number
  • Inversion number
  • Mahonian statistics
  • Major index
  • Polynomials

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