Squares and difference sets in finite fields

C. Bachoc, M. Matolcsi, I. Ruzsa

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

For infinitely many primes p = 4k + 1 we give a slightly improved upper bound for the maximal cardinality of a set B ⊂ Zp such that the difference set B - B contains only quadratic residues. Namely, instead of the “trivial” bound (Formula Presented) we prove (Formula Presented), under suitable conditions on p. The new bound is valid for approximately three quarters of the primes p = 4k + 1.

Original languageEnglish
Title of host publicationIntegers: Annual Volume 2013
PublisherWalter de Gruyter GmbH
Pages1037-1041
Number of pages5
ISBN (Electronic)9783110298161
ISBN (Print)9783110298116
DOIs
Publication statusPublished - Jan 1 2014

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Difference Set
Galois field
Quadratic residue
Cardinality
Trivial
Valid
Upper bound

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Bachoc, C., Matolcsi, M., & Ruzsa, I. (2014). Squares and difference sets in finite fields. In Integers: Annual Volume 2013 (pp. 1037-1041). Walter de Gruyter GmbH. https://doi.org/10.1515/9783110298161.1037

Squares and difference sets in finite fields. / Bachoc, C.; Matolcsi, M.; Ruzsa, I.

Integers: Annual Volume 2013. Walter de Gruyter GmbH, 2014. p. 1037-1041.

Research output: Chapter in Book/Report/Conference proceedingChapter

Bachoc, C, Matolcsi, M & Ruzsa, I 2014, Squares and difference sets in finite fields. in Integers: Annual Volume 2013. Walter de Gruyter GmbH, pp. 1037-1041. https://doi.org/10.1515/9783110298161.1037
Bachoc C, Matolcsi M, Ruzsa I. Squares and difference sets in finite fields. In Integers: Annual Volume 2013. Walter de Gruyter GmbH. 2014. p. 1037-1041 https://doi.org/10.1515/9783110298161.1037
Bachoc, C. ; Matolcsi, M. ; Ruzsa, I. / Squares and difference sets in finite fields. Integers: Annual Volume 2013. Walter de Gruyter GmbH, 2014. pp. 1037-1041
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