Bounds on the size of Lee-codes

Quasi-Perfect Lee Codes of Radius 2 and Arbitrarily Large Dimension

“…AlBdaiwi et al in [3] enumerated all the alphabet sizes q such that there exists a linear 1-perfect Lee code over Z n q . In [6] H. Astola and Tabus obtained, for small alphabet size q and dimension n, an upper bound of the number of codewords of error correcting Lee codes.…”

Semidefinite programming bounds for Lee codes

“…It can be shown that the bound B L 2 (q, n, d) is equal to the Delsarte bound in the Lee scheme, which was calculated for many instances by Astola and Tabus in [2]. In this paper we consider the bound B L 3 (q, n, d).…”

“…, q − 1 of a regular q-gon. To compute the block diagonalization of M 2,∅ (z), one can use the Delsarte formulas in the Lee scheme [1,2]. Here we give the reduction in terms of representative sets.…”

“…Generally, it is an interesting and nontrivial problem to determine A L q (n, d) for given q, n, d. Quistorff made a table of upper bounds on A L q (n, d) based on analytic arguments [20]. H. Astola and I. Tabus calculated several new upper bounds by linear programming [2], using an adaptation of the classical Delsarte bound based on pairs of codewords [9] (see also [1]).…”

“…We find several new upper bounds on A L q (n, d), see Table 1. [2]. The superscript b refers to a bound from Quistorff [20].…”