On $[[n,n-4,3]{]}_q$ Quantum MDS Codes for odd prime power $q$

Abstract

For each odd prime power $q$, let $4\le n\le q^2+1$. Hermitian self-orthogonal $[n,2,n-1]$ codes over $GF(q^2)$ with dual distance three are constructed by using finite field theory. Hence, $[[n,n-4,3]{]}_q$ quantum MDS codes for $4\le n\le q^2+1$ are obtained.

7 pages, submitted to IEEE Trans. Inf. Theory

References in corpus (4)

• Quantum error-correcting codes associated with graphs
• On optimal quantum codes
• Quantum generalized Reed-Solomon codes: Unified framework for quantum MDS codes
• Graphical Nonbinary Quantum Error-Correcting Codes

Cited by in corpus (7)

• Quantum MDS Codes over Small Fields
• Quantum Codes of Maximal Distance and Highly Entangled Subspaces
• Near MDS and near quantum MDS codes via orthogonal arrays
• Constructions of q-ary entanglement-assisted quantum MDS codes with minimum distance greater than q + 1
• Application of Constacyclic codes to Quantum MDS Codes
• New non-binary quantum codes from skew constacyclic codes over the ring ${\mathbb{F}}_{p^m}+v{\mathbb{F}}_{p^m}+v^2{\mathbb{F}}_{p^m}$
• New quantum MDS codes derived from constacyclic codes