A simple polynomial for a transposition over finite fields

2023/12/14 by Al-Maktry, Amr Ali Abdulkader
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2312.08921

Abstract

Let q>2, and let a and b be two elements of the finite field \mathbbF_q with a≠ 0. Carlitz represented the transposition (0a) by a polynomial of degree (q-2)³. In this note, we represent the transposition (ab) by a polynomial of degree q-2. Also, we use this polynomial to construct polynomials that represent permutations of finite local rings with residue field \mathbbF_q.

Related

• Permutation polynomials over finite fields by the local criterion
• Permutation polynomials of finite fields
• Some permutation polynomials via linear translators
• Connecting two types of representations of a permutation of \F_q
• A simple polynomial for a simple transposition