On q-ary Codes with Two Distances d and d + 1

New bounds on D-ary optimal codes

We propose a simple method that, given a symbol distribution, yields upper and lower bounds on the average code length of a D-ary optimal code over that distribution. Thanks to its simplicity, the method permits deriving analytical bounds for families of parametric distributions. We demonstrate this by obtaining new bounds, much better than the existing ones, for Zipf and exponential distributi...

New q-ary quantum MDS codes with distances bigger than \(\frac{q}{2}\)

Constructions of quantum MDS codes have been studied by many authors. We refer to the table in page 1482 of [3] for known constructions. However there have been constructed only a few q-ary quantum MDS [[n, n−2d+2, d]]q codes with minimum distances d > q 2 for sparse lengths n > q + 1. In the case n = q 2 −1 m where m|q + 1 or m|q − 1 there are complete results. In the case n = q 2 −1 m while m...

Constructing new q-ary quantum MDS codes with distances bigger than q/2 from generator matrices

The construction of quantum error-correcting codes has been an active field of quantum information theory since the publication of [1, 2, 3]. It is becoming more and more difficult to construct some new quantum MDS codes with large minimum distance. In this paper, based on the approach developed in the paper [4], we construct several new classes of quantum MDS codes. The quantum MDS codes exhib...

On new completely regular q-ary codes

In this paper from q-ary perfect codes new completely regular q-ary codes are constructed. In particular, two new ternary completely regular codes are obtained from ternary Golay [11, 6, 5] code. The first [11, 5, 6] code with covering radius ρ = 4 coincides with the dual Golay code and its intersection array is (22, 20, 18, 2, 1; 1, 2, 9, 20, 22) . The second [10, 5, 5] code, with covering rad...

Nonequivalent q-ary Perfect Codes