Codes over the Dickson Near-Field of Order Nine
Abstract
A near-field is an algebraic structure akin to a division ring where distributivity is relaxed on one side. The smallest such object is the Dickson near-field of order nine. We lay the foundations of linear codes over that near-field. This includes a systematic form for their generator matrices based on a one-sided Gauss pivot algorithm. Dual codes are defined and a formula is given for the parity check matrix. LCD codes are characterized by a direct sum property. Self-orthogonal codes are classified in short lengths.
Fields of Study & Subjects
Coding theory and cryptography
Digital Filter Design and Implementation
Advanced Wireless Communication Techniques
Publication details
- Journal / source
- Mathematics
- Volume
- 14
- Issue
- 2
- Pages
- 228–228
- Publication date
- 7 January 2026
- Language
- EN