Codes from symmetric polynomials
Mrinmoy Datta, Trygve Johnsen
TL;DR
This paper introduces a new class of error-correcting codes derived from elementary symmetric functions, analyzing their parameters and weight spectra in basic cases to advance coding theory.
Contribution
It defines Reed-Muller type codes from symmetric polynomials and determines their parameters and weight spectra in simple instances, a novel approach in coding theory.
Findings
Determined code parameters for simple cases.
Analyzed higher weight spectra of the codes.
Introduced codes based on elementary symmetric functions.
Abstract
We define and study a class of Reed-Muller type error-correcting codes obtained from elementary symmetric functions in finitely many variables. We determine the code parameters and higher weight spectra in the simplest cases.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · DNA and Biological Computing