PreprintCC BY-NC-ND 4.0arXiv
Multi-sequences with large linear and error linear complexity from function fields
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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BibTeX
@misc{hu2026multisequences,
title = {{Multi-sequences with large linear and error linear complexity from function fields}},
author = {Xubin Hu and Shu Liu and Liming Ma and Chaoping Xing},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17381},
eprint = {2609.17381},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17381},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Multi-sequences with large linear and error linear complexity from function fields
AU - Xubin Hu
AU - Shu Liu
AU - Liming Ma
AU - Chaoping Xing
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17381
UR - https://arxiv.org/abs/2609.17381
AB - 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.
ER -