Hermitian Dickson Dualities for Codes over Near-Fields
Abstract
A Dickson near-field is obtained from Fp2 by twisting multiplication so that distributivity holds only on the right. In this work, we develop a basic theory of right-linear codes of length n over NF(p2). We show that every right-linear code is right-monomially equivalent to a code with a systematic generator matrix, obtained via one-sided row operations. Using Galois conjugation, we introduce the Hermitian Dickson inner product and define the associated dual code, giving an explicit parity-check description in the Fp-systematic case. We also provide effective criteria for Hermitian Dickson LCD, self-orthogonal, and self-dual codes, and we classify Hermitian Dickson self-orthogonal codes in short lengths.
Fields of Study & Subjects
Coding theory and cryptography
Rings
Modules
and Algebras
Cryptography and Residue Arithmetic
Publication details
- Journal / source
- Mathematics
- Volume
- 14
- Issue
- 5
- Pages
- 833–833
- Publication date
- 28 February 2026
- Language
- EN