### Abstract

Given a cubic equation x_{1}y_{1}z_{1} + x _{2}y_{2}z_{2} + ⋯ + x_{n}y _{n}z_{n} = 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 language | English (US) |
---|---|

Pages (from-to) | 1-9 |

Number of pages | 9 |

Journal | Electronic Journal of Combinatorics |

Volume | 8 |

Issue number | 1 R |

State | Published - Dec 1 2001 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

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

### Cite this

*Electronic Journal of Combinatorics*,

*8*(1 R), 1-9.

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*Electronic Journal of Combinatorics*, vol. 8, no. 1 R, pp. 1-9.

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - On coset coverings of solutions of homogeneous cubic equations over finite fields

AU - Aleksanyan, Ara

AU - Papikian, Mihran

PY - 2001/12/1

Y1 - 2001/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=4043135725&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4043135725&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:4043135725

VL - 8

SP - 1

EP - 9

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

SN - 1077-8926

IS - 1 R

ER -