An Algorithm for Computing $m$-Tight Error Linear Complexity of Sequences over $GF(p^{m})$ with Period $p^{m}$

TL;DR

This paper introduces an efficient algorithm to compute the $m$-tight error linear complexity of sequences over GF(p^m) with period p^m, enhancing the analysis of sequence randomness.

Contribution

It presents the first algorithm specifically for calculating $m$-tight error linear complexity of sequences over GF(p^m), extending previous $k$-error complexity methods.

Findings

Algorithm is valid and efficient.

Implemented in C language.

Illustrated with a practical example.

Abstract

The linear complexity (LC) of a sequence has been used as a convenient measure of the randomness of a sequence. Based on the theories of linear complexity, $k$-error linear complexity, the minimum error and the $k$-error linear complexity profile, the notion of $m$-tight error linear complexity is presented. An efficient algorithm for computing $m$-tight error linear complexity is derived from the algorithm for computing $k$-error linear complexity of sequences over GF($p^{m}$) with period $p^n$, where $p$ is a prime. The validity of the algorithm is shown. The algorithm is also realized with C language, and an example is presented to illustrate the algorithm.