Cyclic Sieving for cyclic codes

Alex Mason; Victor Reiner; Shruthi Sridhar

doi:10.1016/j.ffa.2021.101846

Cyclic Sieving for cyclic codes

Alex Mason
, Victor Reiner
, Shruthi Sridhar

School of Mathematics

Research output: Contribution to journal › Article › peer-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 F_q, 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 language	English (US)
Article number	101846
Journal	Finite Fields and their Applications
Volume	73
DOIs	https://doi.org/10.1016/j.ffa.2021.101846
State	Published - Aug 2021

Bibliographical note

Publisher Copyright:
© 2021 Elsevier Inc.

Keywords

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

Publisher link

10.1016/j.ffa.2021.101846

Find It

Find It at U of M Libraries

Cite this

@article{d2134990128e42fdb4a383dc1cde711c,

title = "Cyclic Sieving for cyclic codes",

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.",

keywords = "Cyclic codes, Cyclic sieving, Descent number, Inversion number, Mahonian statistics, Major index, Polynomials",

author = "Alex Mason and Victor Reiner and Shruthi Sridhar",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

year = "2021",

month = aug,

doi = "10.1016/j.ffa.2021.101846",

language = "English (US)",

volume = "73",

journal = "Finite Fields and their Applications",

issn = "1071-5797",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Cyclic Sieving for cyclic codes

AU - Mason, Alex

AU - Reiner, Victor

AU - Sridhar, Shruthi

PY - 2021/8

Y1 - 2021/8

N2 - 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.

AB - 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.

KW - Cyclic codes

KW - Cyclic sieving

KW - Descent number

KW - Inversion number

KW - Mahonian statistics

KW - Major index

KW - Polynomials

UR - https://www.scopus.com/pages/publications/85104082866

UR - https://www.scopus.com/pages/publications/85104082866#tab=citedBy

U2 - 10.1016/j.ffa.2021.101846

DO - 10.1016/j.ffa.2021.101846

M3 - Article

AN - SCOPUS:85104082866

SN - 1071-5797

VL - 73

JO - Finite Fields and their Applications

JF - Finite Fields and their Applications

M1 - 101846

ER -

Cyclic Sieving for cyclic codes

Abstract

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this