Double Toeplitz codes and their average weight enumerators
This work addresses theoretical coding theory problems for researchers in error-correcting codes, but it is incremental as it builds on existing generalizations.
The paper studies average weight enumerators of double Toeplitz codes, a generalization of double circulant codes, and applies this to investigate the existence and classification of such codes with specified minimum weights over finite fields for small lengths and field sizes.
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 $q \in \{2,3,4\}$.