Formation of non-binary Gordon — Mills — Welch sequences in finite fields with arbitrary expansion
Abstract
Abstract. By modifying the algorithm for generating non-binary Gordon — Mills — Welch sequences (GMWS) in finite fields GF( p S ), where S = mn ( m, n > 1), an algorithm for building GMWS for p ≥ 5 with an arbitrary degree of expansion S of the field GF( p ) is developed. It is shown that for simple GF( p ) fields in which the Euler function φ( p – 1) > 1, it is possible to form non-binary GMWS in the extended GF( p S ) fields, where the parameter S can be either a composite or a prime number. The vectors of decimation indices for forming GMWS in the GF(5 2 ), GF(5 3 ), GF(7 2 ), GF(7 3 ), GF(11 2 ), GF(11 3 ) fields are given, as well as the values of the equivalent linear complexity l S of these sequences.
Fields of Study & Subjects
Coding theory and cryptography
Cryptography and Residue Arithmetic
graph theory and CDMA systems
Publication details
- Journal / source
- Известия высших учебных заведений. Приборостроение
- Volume
- 69
- Issue
- 1
- Pages
- 5–12
- Publication date
- 14 February 2026
- Language
- EN