Cyclotomic construction of strong external difference families in finite fields

DOI10.1007/s10623-017-0384-yzbMath1384.05054arXiv1701.01796OpenAlexW2576182392MaRDI QIDQ1744023

Fang-Wei Fu, Minghui Yang, Jiejing Wen, Ke Qin Feng

Publication date: 16 April 2018

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.01796

zbMATH Keywords

finite fielddifference setpartial difference setcyclotomic numbercyclotomic classstrong algebraic manipulation detection codestrong external difference family

Mathematics Subject Classification ID

Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10) Cyclotomy (11T22)

Related Items (10)

Construction and nonexistence of strong external difference families ⋮ Existence and non-existence results for strong external difference families ⋮ Weighted external difference families and R-optimal AMD codes ⋮ Nonexistence of strong external difference families in abelian groups of order being product of at most three primes ⋮ Algebraic manipulation detection codes via highly nonlinear functions ⋮ Strong external difference families in abelian and non-abelian groups ⋮ Some results on generalized strong external difference families ⋮ Some nonexistence results for \((v,m,k,pq)\)-strong external difference families ⋮ On optimal weak algebraic manipulation detection codes and weighted external difference families ⋮ Internal and external partial difference families and cyclotomy

Cites Work

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• Partial difference sets
• Uniform cyclotomy
• A survey of partial difference sets
• Strongly regular Cayley graphs with \(\lambda-\mu=-1\)
• New existence and nonexistence results for strong external difference families
• Paley partial difference sets in groups of order \(n^{4}\) and \(9n^{4}\) for any odd \(n>1\)
• Near-complete external difference families
• Existence and non-existence results for strong external difference families
• Some Nonexistence Results for Strong External Difference Families Using Character Theory

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