#finite fields
9 resultsOn the Sparseness of Certain MRD Codes
Heide Gluesing-Luerssen
The paper calculates how many 3‑dimensional 3×3 maximum rank distance (MRD) codes exist over a finite field and shows that, as the field size grows, MRD codes become increasingly r…
On a theorem of Hegyvári and Hennecart
Dao Nguyen Van Anh, Le Quang Ham, Doowon Koh +2
The paper investigates how product sets grow in the Heisenberg group over finite fields and the complex numbers, providing improved and extended results compared to earlier work by…
Constructive asymptotic bounds of locally repairable codes via function fields
Liming Ma, Chaoping Xing
The paper presents an explicit asymptotic construction of locally repairable codes over any finite field using local expansions of functions at a rational place, achieving a Tsfasm…
On the factorization of iterated polynomials
Lucas Reis
The paper studies how the irreducible factors of composed polynomials f(g⁽ⁿ⁾(x)) over a finite field 𝔽_q grow as n increases, giving new asymptotic bounds for the largest factor d…
Distance Distribution to Received Words in Reed-Solomon Codes
Jiyou Li, Daqing Wan
The paper derives new bounds for counting how many low-degree polynomials added to a given polynomial produce exactly r roots over a finite field, extending previous explicit formu…
Exponential sum estimates over prime fields
Doowon Koh, Mozhgan Mirzaei, Thang Pham +1
The paper extends recent results on multiple character sums by providing new exponential sum estimates for general families of polynomials over prime fields, using the concept of p…
Neighborhood of the supersingular elliptic curve isogeny graph at $j=0$ and $1728$
Songsong Li, Yi Ouyang, Zheng Xu
The paper characterizes the local structure of the ℓ‑isogeny graph of supersingular elliptic curves over \(\mathbb{F}_{p^2}\) around the vertices with j‑invariants 0 and 1728, unde…
Necessities and sufficiencies of a class of permutation polynomials over finite fields
Xiaogang Liu
The paper determines exact necessary and sufficient conditions for polynomials of the form \((x^{2^m}+x+\delta)^{s}+c x\) to be permutation polynomials over the finite field \(\mat…
Inductive algebras for the affine group of a finite field
Promod Sharma, M. K. Vemuri
The paper proves that each irreducible representation of the affine group over a finite field has a unique maximal inductive algebra, and that this algebra is self‑adjoint.