It is known that there is no extremal singly even self-dual [n, n/2, d] code with minimal shadow for (n, d) = (24m+2, 4m+4), (24m+4, 4m+4), (24m+6, 4m+4), (24m + 10, 4m + 4) and (24m + 22, 4m + 6). In this paper, we study singly even self-dual codes with minimal shadow having minimum weight d− 2 for these (n, d). For n = 24m + 2, 24m + 4 and 24m + 10, we show that the weight enumerator of a sin...

Recently, a comprehensive examination of self-dual codes over the alphabet lF2 + ulF2 was published. This included a classification of all self-dual codes up to length 8, and tables of extremal codes up to length 36 for Type I codes and length 40 for Type II codes. Explicit constructions were given except for the Type I code of length 16. A construction for this code is given here. The introduc...

A class of generalized state realizations of codes is introduced. In the graph of such a realization, leaf edges represent symbols, ordinary edges represent states, and vertices represent local constraints on incident edges. Such a graph can be decoded by any version of the sum-product algorithm. Any factor graph representation of a code can be put into this form, and any generalized state real...

In this paper we present a specialized matrix factorization procedure for computing the dual step in a primal-dual path-following interior point algorithm for solving two-stage stochastic linear programs with restricted recourse. The algorithm, based on the Birge-Qi factorization technique, takes advantage of both the dual block-angular structure of the constraint matrix and of the special stru...

In this work a library for solving manipulator motion planning problems has been developed and an algorithm for imposing Cartesian constraints in single arm and dual arm operation has been proposed. The main algorithm is based on RRT [1]. The code has been tested with several single arm and dual arm robots. Our method is able to find collision free paths in environments occupied with obstacles....

A complete classification is given of all [22, 111 and [24, 121 binary self-dual codes. For each code we give the order of its group, the number of codes equivalent to it, and its weight distribution. There is a unique [24, 12, 61 selfdual code. Several theorems on the enumeration of self-dual codes are used, including formulas for the number of such codes with minimum distance > 4, and for the...

A binary linear code is called LCD if it intersects its dual trivially. We show that the coefficients of the joint weight enumerator of such a code with its dual satisfy linear constraints, leading to a new linear programming bound on the size of an LCD code of given length and minimum distance. In addition, we show that this polynomial is, in general, an invariant of a matrix group of dimensio...

We consider codes in the Hamming association scheme Hn (q) with interesting metric properties. We describe how a uniformly packed linear code C determines a pair of dual subschemes. The existence of this pair of sub schemes is used to establish restrictions on the possible distances between codewords in the dual code C.L. These restrictions also apply to arbitrary codes with degree e + 1 and st...

It is shown that the extended quadratic residue code of length 20 over GF(7) is a unique self-dual [20, 10, 9] code C such that the lattice obtained from C by Construction A is isomorphic to the 20-dimensional unimodular lattice D 20, up to equivalence. This is done by converting the classification of such self-dual codes to that of skew-Hadamard matrices of order 20.