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arXiv · 2609.17381

Multi-sequences with large linear and error linear complexity from function fields

Xubin Hu·Shu Liu·Liming Ma·Chaoping Xing
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Abstract

The linear complexity and the error linear complexity of multi-sequences are measures for security in stream ciphers. In this manuscript, we present a general framework for constructing periodic multi-sequences via function fields. We prove that the constructed multi-sequences possess both large linear complexity and large error linear complexity. We apply this framework of constructing multi-sequences to various maximal function fields and we obtain many new multi-sequences with various lengths and dimensions. As a byproduct, we adopt this idea and produce many new quasi-cyclic algebraic geometric codes as well.

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Xubin Hu, Shu Liu, Liming Ma, Chaoping Xing. 2026-09-15. Multi-sequences with large linear and error linear complexity from function fields. https://arxiv.org/abs/2609.17381

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