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Certain diagonal equations and conflict-avoiding codes of prime lengths.
- Source :
-
Finite Fields & Their Applications . Dec2023, Vol. 92, pN.PAG-N.PAG. 1p. - Publication Year :
- 2023
-
Abstract
- We study the construction of optimal conflict-avoiding codes (CAC) from a number theoretical point of view. The determination of the size of optimal CAC of prime length p and weight 3 is formulated in terms of the solvability of certain twisted Fermat equations of the form g 2 X ℓ + g Y ℓ + 1 = 0 over the finite field F p for some primitive root g modulo p. We treat the problem of solving the twisted Fermat equations in a more general situation by allowing the base field to be any finite extension field F q of F p. We show that for q greater than a lower bound of the order of magnitude O (ℓ 2) there exists a generator g of F q × such that the equation in question is solvable over F q. Using our results we are able to contribute new results to the construction of optimal CAC of prime lengths and weight 3. [ABSTRACT FROM AUTHOR]
- Subjects :
- *FINITE fields
*EQUATIONS
*PROBLEM solving
*BINARY sequences
Subjects
Details
- Language :
- English
- ISSN :
- 10715797
- Volume :
- 92
- Database :
- Academic Search Index
- Journal :
- Finite Fields & Their Applications
- Publication Type :
- Academic Journal
- Accession number :
- 173235548
- Full Text :
- https://doi.org/10.1016/j.ffa.2023.102298