New Binary Quantum Codes Constructed from Quasi-Cyclic Codes

Abstract

It is well known that quantum codes can be constructed by means of classical symplectic dual-containing codes. This paper considers a family of twogenerators quasi-cyclic codes and derives sufficient conditions for these codes to be dual-containing. Then, a new method for constructing binary quantum codes is proposed. As an application, we construct 11 binary quantum codes that exceed the beak-known results. Further, another 40 new binary quantum codes are obtained by propagation rules, all of which improve the lower bound on the minimum distance.

On construction of quantum codes with dual-containing quasi-cyclic codes

“…gcd(g2(x),t(x)) ), lcm(t(x)g 2 (x), g 1 (x)t 2 (x)))) d(gcd(lcm(g 2 (x), g1(x) gcd(g1(x),t(x)) ), lcm(g 2 (x)t 2 (x), t(x)g 1 (x)))). [ [18,4,6]] 4 -[ [18,4,5]] 4 [22,16,6] 16 [[22, 10, 6]] 4 -[ [22,8,6]] 4 [26,16,8] 16 [[26, 6, 8]] 4 -- [26,17,7] 16 [[26, 8, 7]] 4 --[30, 23,6] 16 [[30, 16, 6]] 4 [[31, 16, 5]] 4 -[30, 24,5] 16 [[30, 18, 5] [12,9,4] 25 [[12, 6, 4]] 5 -[ [16,6,4]]5 [14,7,7] 25 [[14, 0, 7]] 5 -- [14,8,6] 25 [[14, 2, 6]] 5 -[ [19,1,5]] 5 [16,8,8] 25 [[16, 0, 8]] 5 -- [16,…”

“…In 2018, Galindo et al [15] proposed an original method to construct quantum codes employing quasi-cyclic codes, which attracted many authors to devote themselves to the investigation of quasicyclic codes to construct QECCs. Thereby, a series of record-breaking QECCs were constructed by quasi-cyclic codes [16][17][18][19][20][21][22][23][24].…”