Double Toeplitz codes and their average weight enumerators

Abstract

Recently, double Toeplitz codes have been introduced as a generalization of double circulant codes. In this paper, we study the average weight enumerators of double Toeplitz codes. As an application, we consider the existence of double Toeplitz codes over $\mathbb{F}_q$ with some specified minimum weights for $q \in \{2,3,4\}$. We also give a classification of double Toeplitz codes over $\mathbb{F}_q$ with the largest minimum weights for modest lengths and $q \in \{2,3,4\}$.

Theorems & Definitions (22)

• Proposition 2.1: Shi, Xu and Solé SXS
• Theorem 3.1: SXS
• Lemma 3.2
• proof
• Theorem 3.3
• proof
• Proposition 3.4
• proof
• Lemma 4.1
• proof