2021/10/02 by Sok, Lin
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2110.00769
There has been a lot of effort to construct good quantum codes from the classical error correcting codes. Constructing new quantum codes, using Hermitian self-orthogonal codes, seems to be a difficult problem in general. In this paper, Hermitian self-orthogonal codes are studied from algebraic function fields. Sufficient conditions for the Hermitian self-orthogonality of an algebraic geometry code are presented. New Hermitian self-orthogonal codes are constructed from projective lines, elliptic curves, hyper-elliptic curves, Hermitian curves, and Artin-Schreier curves. In addition, over the projective lines, we construct new families of MDS quantum codes with parameters [[N,N-2K,K+1]]q under the following conditions: i) N=t(q-1)+1 or t(q-1)+2 with t|(q+1) and K=\lfloor(t(q-1)+1)/(2t)\rfloor+1; ii) (n-1)|(q2-1), N=n or N=n+1, K0=\lfloor(n+q-1)/(q+1)\rfloor, and K≥ K0+1; iii) N=tq+1, ∀~1≤ t≤ q and K=\lfloor(tq+q-1)/(q+1)\rfloor+1; iv) n|(q2-1), n2=(n)/(gcd (n,q+1)), ∀~ 1≤ t≤ (q-1)/(n2)-1, N=(t+1)n+2 and K=\lfloor ((t+1)n+1+q-1)/(q+1)\rfloor+1.