A new construction of quantum error-correcting codes
Keqin Feng, Chaoping Xing · Transactions of the American Mathematical Society · 2007
In this paper, we present a characterization of (binary and non-binary) quantum error-correcting codes. Based on this characterization, we introduce a method to construct p p -ary quantum codes using Boolean functions satisfying a system of certain quadratic relations. As a consequence of the construction, we are able to construct quantum codes of minimum distance 2 2 . In particular, we produce a class of binary quantum ( ( n , 2 n − 2 − 1 2 ( n − 1 ( n − 1 ) / 2 ) , 2 ) ) ((n,2^{n-2}-\frac 12{n-1\choose (n-1)/2},2)) -codes for odd length n ≥ 5 n\ge 5 . For n ≥ 11 n\ge 11 , this improves the result by Rains in Quantum codes of minimal distance two , 1999, showing the existence of binary quantum ( ( n , 3 ⋅ 2 n − 4 , 2 ) ) ((n,3\cdot 2^{n-4},2)) -codes for odd n ≥ 5 n\ge 5 . Moreover, our binary quantum