We generalize the Griesmer bound in the case of systematic codes over a field of size q greater than the distance d of the code. We also generalize the Griesmer bound in the case of any systematic code of distance 2,3,4 and in the case of binary systematic codes of distance up to 6.

Today we’ll describe a new family of codes, called algebraic-geometry codes. These codes generalize Reed-Solomon codes and yield surprisingly good codes over constant sized alphabets. We’ll motivate the codes from two points of view. First we’ll show how they challenge the “conjectured converse of the Gilbert-Varshamov bound”. We’ll then motivate the codes from the algebraic perspective. The re...

New quaternary Plotkin constructions are given and are used to obtain new families of quaternary codes. The parameters of the obtained codes, such as the length, the dimension and the minimum distance are studied. Using these constructions new families of quaternary Reed-Muller codes are built with the peculiarity that after using the Gray map the obtained Z4-linear codes have the same paramete...

In an earlier paper the author defined N1L configurations, and stated a conjecture concerning them which would lead to an improvement by a constant factor to the sphere-packing bound for linear double error correcting codes. Here a computer search is presented, in an effort to gather evidence on the conjecture.

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...

We consider active, semi-supervised learning in an offline transductive setting. We show that a previously proposed error bound for active learning on undirected weighted graphs can be generalized by replacing graph cut with an arbitrary symmetric submodular function. Arbitrary non-symmetric submodular functions can be used via symmetrization. Different choices of submodular functions give diff...

Two approaches addressing response surface approximation errors due to model inadequacy (bias error) are presented, and a design of experiments minimizing the maximal bias error is proposed. Both approaches assume that the functional form of the true model is known and seek, at each point in design space, worst case bounds on the absolute error. The first approach is implemented prior to data g...

in this work, a new iterative method is proposed for obtaining the approximate solution of a class of hammerstein type integral equations system. the main structure of this method is based on the richardson iterative method for solving an algebraic linear system of equations. some conditions for existence and unique solution of this type equations are imposed. convergence analysis and error bou...

We solve the problem of the classification of perfect quantum codes. We prove that the only nontrivial perfect quantum codes are those with the parameters ( ( 2 2 2 ( 1) ( 1) , ,3 l n q q q q − − − )) l . There exist no other nontrivial perfect quantum codes.

A reduction in error is obtained for estimates of range computed in a multipath environment. A good estimation technique for this problem typically involves exploiting the mul-tipath interference, that is, analyzing each received signal reeection to improve the estimate. Under certain conditions , however, the errors in multipath estimates can be quite large. We compute the Cram er-Rao bounds f...