Codes induced by alternative codes

TL;DR

This paper studies codes induced by alternative codes, exploring their properties, subclasses, and providing an algorithm to determine if a finite code is alt-induced, extending the theory of ordinary codes.

Contribution

It introduces characteristic properties of alt-induced codes, analyzes subclasses, and proposes an algorithm for finite code classification.

Findings

Established properties of alt-induced codes

Analyzed subclasses of alt-induced codes

Proposed an algorithm to identify finite alt-induced codes

Abstract

Alternative codes, an extension of the notion of ordinary codes, have been first introduced and considered by P. T. Huy et al. in 2004. As seen below, every alternative code, in its turn, defines an ordinary code. Such codes are called codes induced by alternative codes or alt-induced codes, for short. In this paper we consider these alt-induced codes and subclasses of them. In particular, characteristic properties of such codes are established, and an algorithm to check whether a finite code is alt-induced or not is proposed.