Cumulative-Separable Codes

TL;DR

This paper studies q-ary cumulative-separable codes, exploring their relationships and providing improved bounds on their minimum distance and dimension.

Contribution

It introduces new insights into the structure of cumulative-separable codes and refines bounds on their parameters.

Findings

Demonstrates relations between different codes in the class.

Provides improved bounds for minimum distance.

Provides improved bounds for code dimension.

Abstract

q-ary cumulative-separable $\Gamma(L,G^{(j)})$-codes $L=\{ \alpha \in GF(q^{m}):G(\alpha )\neq 0 \}$ and $G^{(j)}(x)=G(x)^{j}, 1 \leq i\leq q$ are considered. The relation between different codes from this class is demonstrated. Improved boundaries of the minimum distance and dimension are obtained.