A class of punctured simplex codes which are proper for error detection

TL;DR

This paper investigates a specific class of binary linear codes, demonstrating their effectiveness for error detection across many previously unresolved parameter combinations, thus advancing coding theory.

Contribution

It introduces and analyzes a particular class of [n,k] codes, proving their propriety for error detection in many cases where existence was previously uncertain.

Findings

Codes are proper for many new (n,k) combinations

Extends known classes of error-detecting codes

Provides evidence supporting the conjecture on code existence

Abstract

Binary linear [n,k] codes that are proper for error detection are known for many combinations of n and k. For the remaining combinations, existence of proper codes is conjectured. In this paper, a particular class of [n,k] codes is studied in detail. In particular, it is shown that these codes are proper for many combinations of n and k which were previously unsettled.