DNA sequences generated by ℤ4-linear codes

New upper bounds on binary linear codes and a ℤ4-code with a better-than-linear Gray image

Using integer linear programming and table-lookups we prove that there is no binary linear [1988, 12, 992] code. As a byproduct, the non-existence of binary linear [324, 10, 160], [356, 10, 176], [772, 11, 384], and [836, 11, 416] codes is shown. On the other hand, there exists a linear (994, 4, 992) code over Z4. Its Gray image is a binary non-linear (1988, 2, 992) code. Therefore, we can add ...

ℤ4-codes and their Gray map images as orthogonal arrays

A classic result of Delsarte connects the strength (as orthogonal array) of a linear code with the minimum weight of its dual: the former is one less than the latter. Since the paper of Hammons et al., there is a lot of interest in codes over rings, especially in codes over Z4 and their (usually non-linear) binary Gray map images. We show that Delsarte’s observation extends to codes over arbitr...

On ℤ4 codes satisfying the chain condition

Centralizer algebras of the group associated to ℤ4-codes

The purpose of this paper is to investigate the finite group which appears in the study of the Type II Z4-codes. To be precise, it is characterized in terms of generators and relations, and we determine the structure of the centralizer algebras of the tensor representations of this group.

Ancient DNA sequence revealed by error-correcting codes

A previously described DNA sequence generator algorithm (DNA-SGA) using error-correcting codes has been employed as a computational tool to address the evolutionary pathway of the genetic code. The code-generated sequence alignment demonstrated that a residue mutation revealed by the code can be found in the same position in sequences of distantly related taxa. Furthermore, the code-generated s...