Some connections between binary block codes and Hilbert algebras

TL;DR

This paper explores the relationship between Hilbert algebras and binary block-codes, demonstrating how codes can generate examples of specific algebra classes with certain properties.

Contribution

It introduces a method to construct classes of Hilbert algebras using binary block-codes, highlighting new connections between coding theory and algebraic structures.

Findings

Binary block-codes can determine orders in Hilbert algebras.

Examples of semisimple and local Hilbert algebras are constructed using codes.

Codes facilitate the analysis of algebraic properties.

Abstract

In this paper, we will study some connections between Hilbert al- gebras and binary block-codes.With these codes, we can eassy obtain orders which determine suplimentary properties on these algebras. We will try to emphasize how, using binary block-codes, we can provide examples of classes of Hilbert algebras with some properties, in our case, classes of semisimple Hilbert algebras and classes of local Hilbert algebras.