For an [n, k, d]q code C, we define a mapping wC from PG(k − 1, q) to the set of weights of C via a generator matrix of C. We give a geometric aspect derived from wC to investigate the extendability of linear codes. We survey known extension theorems and some recent results.

GivenS|R a finite Galois extension of finite chain rings andB anS-linear code we define twoGalois operators, the closure operator and the interior operator. We proof that a linear code is Galois invariant if and only if the row standard form of its generator matrix has all entries in the fixed ring by the Galois group and show a Galois correspondence in the class of S-linear codes. As applicati...

We show that there is no [24, 12, 9] doubly-even self-dual code over F4 by attempting to construct the generator matrix of this code directly.

The problem of decoding a binary linear code used over a binary symmetric channel so as to minimize bit error probability, rather than codeword error probability, is studied. In general, there are substantial differences with the maximum likelihood case. The optimal decoding rule depends on the crossover probability of the channel, the bit error probability depends on the generator matrix used,...

We describe a system for determining a random palette providing color juxtaposition in digital images, both synthetic and scanned. The result can be significantly increased visual richness and sophistication in color usage. The Generalized Impressionistic Texture Matrix Generator F. Kenton Musgrave Myeong Lim The George Washington University 20101 Academic Way Ashburn, VA 22011 (703) 729-8254 (...

In this paper we identify conditions under which a true generator does or does not exist for an empirically observed Markov transition matrix. We show how to search for valid generators and choose the \correct" one that is the most compatible with bond rating behaviors. We also show how to obtain an approximate generator when a true generator does not exist.

‎‎A natural generalization of two dimensional cyclic code ($T{TDC}$) is two dimensional skew cyclic code‎. ‎It is well-known that there is a correspondence between two dimensional skew cyclic codes and left ideals of the quotient ring $R_n:=F[x,y;rho,theta]/_l$‎. ‎In this paper we characterize the left ideals of the ring $R_n$ with two methods and find the generator matrix for two dimensional s...

The goal of IT governance is not only to achieve internal efficiency in an IT organization, but also to support IT’s role as a business enabler. The latter is here denoted IT governance performance, and cannot be controlled by IT management directly. Their realm of control includes IT governance maturity, indicated by e.g. different IT activities, documents, metrics and roles. Current IT govern...

We present a new tree-level matrix element generator, based on the colour dressed Berends-Giele recursive relations. We discuss two new algorithms for phase space integration, dedicated to be used with large multiplicities and colour sampling.