Constructions of <i>?</i>-Adic <i>t</i>-Deletion-Correcting Quantum Codes

Constructions of good entanglement-assisted quantum error correcting codes

Entanglement-assisted quantum error correcting codes (EAQECCs) are a simple and fundamental class of codes. They allow for the construction of quantum codes from classical codes by relaxing the duality condition and using pre-shared entanglement between the sender and receiver. However, in general it is not easy to determine the number of shared pairs required to construct an EAQECC. In this pa...

On perfect deletion-correcting codes

In this article we present constructions for perfect deletion-correcting codes. The first construction uses perfect deletion-correcting codes without repetition of letters to construct other perfect deletion-correcting codes. This is a generalization of the construction shown in [1]. In the third section we investigate several constructions of perfect deletioncorrecting codes using designs. In ...

On Single-Deletion-Correcting Codes

This paper gives a brief survey of binary single-deletion-correcting codes. The Varshamov-Tenengolts codes appear to be optimal, but many interesting unsolved problems remain. The connections with shift-register sequences also remain somewhat mysterious.

One-point Goppa Codes on Some Genus 3 Curves with Applications in Quantum Error-Correcting Codes

We investigate one-point algebraic geometric codes CL(D, G) associated to maximal curves recently characterized by Tafazolian and Torres given by the affine equation yl = f(x), where f(x) is a separable polynomial of degree r relatively prime to l. We mainly focus on the curve y4 = x3 +x and Picard curves given by the equations y3 = x4-x and y3 = x4 -1. As a result, we obtain exact value of min...

Constructions for Variable-Length Error-Correcting Codes