# On the $k$-error linear complexity of subsequences of $d$-ary Sidel'nikov sequences over prime field $\mathbb{F}_{d}$

## TL;DR

This paper investigates the $k$-error linear complexity of subsequences of $d$-ary Sidel'nikov sequences over prime fields, providing bounds and demonstrating high complexity for certain periods, which is relevant for cryptographic security.

## Contribution

It establishes a general lower bound for the $k$-error linear complexity of these sequences and shows they have large complexity for specific periods, advancing understanding of their cryptographic strength.

## Key findings

- Provided a general lower bound for $k$-error linear complexity.
- Demonstrated sequences have large $k$-error linear complexity for certain periods.
- Enhanced understanding of the cryptographic robustness of $d$-ary Sidel'nikov sequences.

## Abstract

We study the $k$-error linear complexity of subsequences of the $d$-ary Sidel'nikov sequences over the prime field $\mathbb{F}_{d}$. A general lower bound for the $k$-error linear complexity is given. For several special periods, we show that these sequences have large $k$-error linear complexity.