Most coding theory experts date the origin of the subject with the 1948 publication of A
Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has …

We present new constructions of binary quantum codes from quaternary linear Hermitian
self-dual codes. Our main ingredients for these constructions are nearly self-orthogonal …

This paper describes a fundamental correspondence between Boolean functions and
projection operators in Hilbert space. The correspondence is widely applicable, and it is …

Two new constructions of linear code pairs C 2⊂ C 1 are given for which the codimension
and the relative minimum distances M 1 (C 1, C 2) and M 1 (C 2⊥, C 1⊥) are good. By this …

Hybrid codes simultaneously encode both quantum and classical information into physical
qubits. We give several general results about hybrid codes, most notably that the quantum …

Duadic group algebra codes are a generalization of quadratic residue codes. This paper
addresses an open problem raised by Zhu concerning the existence of duadic group …

It is conjectured that quantum computers are able to solve certain problems more quickly
than any deterministic or probabilistic computer. For instance, Shor's algorithm is able to …

The Generalized Hamming weights and their relative version, which generalize the
minimum distance of a linear code, are relevant to numerous applications, including coding …

We present a family of non-CSS quantum stabilizer codes using the structure of duadic
constacyclic codes over $\mathbb {F} _4 $. Within this family, quantum codes can possess …

We construct new families of duadic codes and derive from them degenerate quantum
codes. This provides a solution to a question raised by Aly, Klappenecker and Sarvepalli on …