On Semidefinite Programming Relaxations of Association Schemes With Application to Combinatorial Optimization Problems

AMS classification: 90C22, 20Cxx, 70-08traveling salesman problem;maximum bisection;semidefinite programming;association schemes

On the parameters of codes for the Lee and modular distance

AbstractWe introduce the concept of a weakly metric association scheme, a generalization of metric schemes. We undertake a combinatorial study of the parameters of codes in these schemes, along the lines of [9]. Applications are codes over Zq for the Lee distance and arithmetic codes for the modular distance.Our main result is an inequality which generalizes both the Delsarte upper bound on covering radius, and the MacWilliams lower bound on the external distance, yielding a strong necessary existence condition on completely regular codes.The external distance (in the Lee metric) of some self-dual codes of moderate length over Z5 is computed

可換アソシエーションスキームの拡張について

Tohoku University田中太初課

The Lee association scheme

SIGLECNRS 14802 E / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

On the linear programming bound for linear Lee codes

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 (Formula presented.) 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.publishedVersionPeer reviewe