Lamʼs power residue addition sets

Byard, Kevin; Evans, Ronald J.; Veen, Mark Van

doi:10.1016/j.aam.2010.09.008

Cited by 3 publications

(2 citation statements)

References 23 publications

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“…This contradicts the fact that 3 is not a square, so the matrix equation has no viable solution. Tables 2,3,7,9,10,11,12,13,14,15,23,24 In the general solution, B = 0, which contradicts (2.5). Tables 4,5,6,16,17,18,19,20,21 In the general solution, X is not an integer, which is a contradiction.…”

Section: Tablementioning

confidence: 94%

Nonexistence of twenty-fourth power residue addition sets

Evans

Veen²

2017

Finite Fields and Their Applications

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Let n > 1 be an integer, and let F p denote a field of p elements for a prime p ≡ 1 (mod n). By 2015, the question of existence or nonexistence of n-th power residue difference sets in F p had been settled for all n < 24. We settle the case n = 24 by proving the nonexistence of 24-th power residue difference sets in F p . We also prove the nonexistence of qualified 24-th power residue difference sets in F p . The proofs make use of a Mathematica program which computes formulas for the cyclotomic numbers of order 24 in terms of parameters occurring in quadratic partitions of p.

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Section: Tablementioning

confidence: 94%

Nonexistence of twenty-fourth power residue addition sets

Evans

Veen²

2017

Finite Fields and Their Applications

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“…A remarkable one is that to finite projective planes, which we will illustrate in Subsection 5.3. Physical applications of difference sets can be found in the references listed in [4].…”

Section: Introductionmentioning

confidence: 99%

Cyclotomic difference sets in finite fields

Xia

2018

Math. Comp.

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The classical problem of whether mth-powers with or without zero in a finite field F q form a difference set has been extensively studied, and is related to many topics, such as flag transitive finite projective planes. In this paper new necessary and sufficient conditions are established including those via a system of polynomial equations on Gauss sums. The author thereby solves the problem for even q which is neglected in the literature, and extends the nonexistence list for even m up to 22. Moreover, conjectures toward the complete classification are posed.

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Cyclotomic difference sets in finite fields

Xia

2015

Preprint

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The classical problem of whether mth-powers with or without zero in a finite field Fq form a difference set has been extensively studied, and is related to many topics, such as flag transitive finite projective planes. In this paper new necessary and sufficient conditions are established including those via a system of polynomial equations on Gauss sums. The author thereby solves the problem for even q which is neglected in the literature, and extends the nonexistence list for even m up to 22. Moreover, conjectures toward the complete classification are posed.

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Lamʼs power residue addition sets

Cited by 3 publications

References 23 publications

Nonexistence of twenty-fourth power residue addition sets

Nonexistence of twenty-fourth power residue addition sets

Cyclotomic difference sets in finite fields

Cyclotomic difference sets in finite fields

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