TY - JOUR
T1 - Steane-enlargement of quantum codes from the Hermitian function field
AU - Christensen, René Bødker
AU - Geil, Olav
PY - 2020/2/11
Y1 - 2020/2/11
N2 - In this paper, we study the construction of quantum codes by applying Steane-enlargement to codes from the Hermitian function field. We cover Steane-enlargement of both usual one-point Hermitian codes and of order bound improved Hermitian codes. In particular, the paper contains two constructions of quantum codes whose parameters are described by explicit formulae, and we show that these codes compare favourably to existing, comparable constructions in the literature. Furthermore, a number of the new codes meet or even exceed the quantum Gilbert–Varshamov bound.
AB - In this paper, we study the construction of quantum codes by applying Steane-enlargement to codes from the Hermitian function field. We cover Steane-enlargement of both usual one-point Hermitian codes and of order bound improved Hermitian codes. In particular, the paper contains two constructions of quantum codes whose parameters are described by explicit formulae, and we show that these codes compare favourably to existing, comparable constructions in the literature. Furthermore, a number of the new codes meet or even exceed the quantum Gilbert–Varshamov bound.
KW - algebraiske geometrikoder
KW - kvantekoder
KW - Steane-enlargement
KW - Hermitisk funktionslegeme
KW - algebraic geometric codes
KW - quantum code
KW - Steane-enlargement
KW - Hermitian function field
UR - http://www.scopus.com/inward/record.url?scp=85079418347&partnerID=8YFLogxK
U2 - 10.1007/s10623-019-00709-7
DO - 10.1007/s10623-019-00709-7
M3 - Journal article
SN - 0925-1022
VL - 88
SP - 1639
EP - 1652
JO - Designs, Codes and Cryptography
JF - Designs, Codes and Cryptography
IS - 8
ER -