On coset coverings of solutions of homogeneous cubic equations over finite fields

Ara Aleksanyan, Mihran Papikian

Research output: Contribution to journalArticle

Abstract

Given a cubic equation x1y1z1 + x 2y2z2 + ⋯ + xny nzn = b over a finite field, it is necessary to determine the minimal number of systems of linear equations over the same field such that the union of their solutions exactly coincides with the set of solutions of the initial equation. The problem is solved for arbitrary size of the field. A covering with almost minimum complexity is constructed.

Original languageEnglish (US)
Pages (from-to)1-9
Number of pages9
JournalElectronic Journal of Combinatorics
Volume8
Issue number1 R
StatePublished - Dec 1 2001

Fingerprint

Cubic equation
Coset
Linear equations
Galois field
Covering
System of Linear Equations
Union
Necessary
Arbitrary

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

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On coset coverings of solutions of homogeneous cubic equations over finite fields. / Aleksanyan, Ara; Papikian, Mihran.

In: Electronic Journal of Combinatorics, Vol. 8, No. 1 R, 01.12.2001, p. 1-9.

Research output: Contribution to journalArticle

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