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Linear complexity of non-binary Gordon – Mills – Welch sequences in arbitrary finite fields
https://doi.org/10.17586/0021-3454-2025-68-5-380-387
Abstract
The relations for determining the equivalent linear complexity (ELC) lS of non-binary Gordon — Mills — Welch sequences (GMWS) formed in arbitrary extended finite fields GF[(pm)n] are presented. The values of the ELC of the GMWS for fields with a base p = 3 -17 are obtained, taking into account the parameter Мn(rp) equal to the number of summable sequences during the formation of the GMWS. It is shown that the parameter Мn(rp) depends exclusively on the degree n of the field expansion and the values of the digits of the p-ary representation of the number rp, which is mutually simple with the order of the multiplicative group of the subfield GF(pm).
About the Authors
V. G. Starodubtsev
A. F. Mozhaisky Military Space Academy
Russian Federation
Russian Federation
Victor G. Starodubtsev — PhD., Associate Professor, Department of Technologies and Automation of Processing and Analysis of Spacecraft Information; Senior Lecturer
St. Petersburg
E. B. Samoylov
A. F. Mozhaisky Military Space Academy
Russian Federation
Russian Federation
Evgeny B. Samoylov — PhD, Associate Professor, Department of Technologies and Automation of Processing and Analysis of Spacecraft Information
St. Petersburg
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Review
For citations:
Starodubtsev V.G., Samoylov E.B. Linear complexity of non-binary Gordon – Mills – Welch sequences in arbitrary finite fields. Journal of Instrument Engineering. 2025;68(5):380-387. (In Russ.) https://doi.org/10.17586/0021-3454-2025-68-5-380-387
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