On the linear programming bound for linear Lee codes

Abstract

Based on an invariance-type property of the Lee-compositions of a linear Lee code, additional equality constraints can be introduced to the linear programming problem of linear Lee codes. In this paper, we formulate this property in terms of an action of the multiplicative group of the field on the set of Lee-compositions. We show some useful properties of certain sums of Lee-numbers, which are the eigenvalues of the Lee association scheme, appearing in the linear programming problem of linear Lee codes. Using the additional equality constraints, we formulate the linear programming problem of linear Lee codes in a very compact form, leading to a fast execution, which allows to efficiently compute the bounds for large parameter values of the linear codes.

Software application in mining engineering

“…The main purpose is solving transportation problem using some methods of transportation model by linear programming (LP). Linear programming has already demonstrated its value as an aid to making decision in business, industry, and governmental applications (Ilich, 2008;Qi, Tian, & Shi, 2012;Antipin & Khoroshilova, 2015;Astola & Tabus, 2016). Determination of facility or machine scheduling, distribution of commodities, determination of optimum products mix, and allocation of labor and other resources are few examples of the problems that can be solved by linear programming.…”