Certain diagonal equations and conflict-avoiding codes of prime lengths

Liang Chung Hsia, Hua Chieh Li, Wei Liang Sun*


研究成果: 雜誌貢獻期刊論文同行評審


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 g2X+gY+1=0 over the finite field Fp 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 Fq of Fp. We show that for q greater than a lower bound of the order of magnitude O(ℓ2) there exists a generator g of Fq× such that the equation in question is solvable over Fq. Using our results we are able to contribute new results to the construction of optimal CAC of prime lengths and weight 3.

期刊Finite Fields and their Applications
出版狀態已發佈 - 2023 12月

ASJC Scopus subject areas

  • 理論電腦科學
  • 代數與數理論
  • 一般工程
  • 應用數學


深入研究「Certain diagonal equations and conflict-avoiding codes of prime lengths」主題。共同形成了獨特的指紋。