CRT Based Spectral Convolution in Binary Fields

TL;DR

This paper introduces a CRT-based spectral convolution method for binary fields that reduces computational complexity, enhancing analysis of combinatorial sequences and generator structures.

Contribution

It presents a novel, more efficient convolution technique using the Chinese Remainder Theorem for spectral analysis in binary fields.

Findings

Lower computational complexity compared to existing methods

Effective analysis of combiner generator structures

Significant efficiency improvements in spectral convolutions

Abstract

In this paper, new results on convolution of spectral components in binary fields have been presented for combiatorial sequences. A novel method of convolution of DFT points through Chinese Remainder Theorem (CRT) is presented which has lower complexity as compared to known methods of spectral point computations. Exploring the inherent structures in cyclic nature of finite fields, certain fixed mappings between the spectral components from composite fields to their decomposed subfield components has been illustrated which are significant for analysis of combiner generators. Complexity estimations of our CRT based methodology of convolutions in binary fields proves that our proposed method is far efficient as comparised to to existing methods of DFT computations for convolving sequences in frequency domain.