2 research outputs found
Constructions of q-Ary Constant-Weight Codes
This paper introduces a new combinatorial construction for q-ary
constant-weight codes which yields several families of optimal codes and
asymptotically optimal codes. The construction reveals intimate connection
between q-ary constant-weight codes and sets of pairwise disjoint combinatorial
designs of various types.Comment: 12 page
Mutually unbiased maximally entangled bases from difference matrices
Based on maximally entangled states, we explore the constructions of mutually
unbiased bases in bipartite quantum systems. We present a new way to construct
mutually unbiased bases by difference matrices in the theory of combinatorial
designs. In particular, we establish mutually unbiased bases with
maximally entangled bases and one product basis in for arbitrary prime power . In addition, we construct
maximally entangled bases for dimension of composite numbers of non-prime
power, such as five maximally entangled bases in and , which improve the
known lower bounds for , with in . Furthermore, we construct mutually unbiased bases with
maximally entangled bases and one product basis in for arbitrary prime number .Comment: 24 page