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Formation of non-binary Gordon — Mills — Welch sequences in finite fields with arbitrary expansion
https://doi.org/10.17586/0021-3454-2026-69-1-5-12
Abstract
Abstract. By modifying the algorithm for generating non-binary Gordon — Mills — Welch sequences (GMWS) in finite fields GF(pS), 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(pS) 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(52), GF(53), GF(72), GF(73), GF(112), GF(113) fields are given, as well as the values of the equivalent linear complexity lS of these sequences.
About the Authors
V. G. Starodubtsev
A. F. Mozhaisky Military Space Academy
Russian Federation
Russian Federation
Victor G. Starodubtsev — PhD, Associate Professor; Lecturer
St. Petersburg
V. G. Zinoviev
A. F. Mozhaisky Military Space Academy
Russian Federation
Russian Federation
Valery G. Zinoviev — PhD, Associate Professor; Professor
St. Petersburg
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Review
For citations:
Starodubtsev V.G., Zinoviev V.G. Formation of non-binary Gordon — Mills — Welch sequences in finite fields with arbitrary expansion. Journal of Instrument Engineering. 2026;69(1):5-12. (In Russ.) https://doi.org/10.17586/0021-3454-2026-69-1-5-12
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