New Quantum Codes Constructed by Quantum Caps in PG(3,9) and PG(4,9)

Abstract

In this paper, we present a computer-supported method of searching for quantum caps. By means of this method and relevant knowledge of combinatorics, many quantum caps in $PG(3,9)$ and $PG(4,9)$ are constructively proven to exist. Then, according to the theorem that each quantum cap corresponds to a quantum error-correcting code with $d=4$ , we obtain 278 quantum error-correcting codes. Most of these results break the GV bound, and a number of them are optimal quantum codes or have improved parameters.

Keywords

• Quantum cap
• quantum Hamming bound
• quantum error-correcting code
• combinatorial construction