Computing coset leaders and leader codewords of binary codes

In this paper we use the Gr\"obner representation of a binary linear code $\mathcal C$ to give efficient algorithms for computing the whole set of coset leaders, denoted by $\mathrm{CL}(\mathcal C)$ and the set of leader codewords, denoted by $\mathrm L(\mathcal C)$. The first algorithm could be adapted to provide not only the Newton and the covering radius of $\mathcal C$ but also to determine the coset leader weight distribution. Moreover, providing the set of leader codewords we have a test-set for decoding by a gradient-like decoding algorithm. Another contribution of this article is the relation stablished between zero neighbours and leader codewords

Could and Should America Have Made an Ottoman Republic in 1919?

Numerous Americans, perhaps especially American lawyers, have since the 1780s presumed to tell other peoples how to govern themselves. In 2006, that persistent impulse was once again echoed in an address to the American Bar Association by a Justice of the Supreme Court. The purpose of this essay is to question the wisdom of this evangelical ambition, especially when the form of instruction includes military force. It is draws on Spreading America\u27s Word (2005) and directs attention to the hopes of American Protestant Zionists to make a democratic republic in Ottoman Palestine. It suggests that chances were better in 1919 than they are in 2008, but were none to good at that time. It rejects the appeal of the militant neo-conservatives who expressed their hopes and expectations in The Project for A New American Century, an instrument that should be read and remembered for centuries to come

Families of nested completely regular codes and distance-regular graphs

In this paper infinite families of linear binary nested completely regular codes are constructed. They have covering radius $\rho$ equal to $3$ or $4$, and are $1/2^i$-th parts, for $i\in\{1,\ldots,u\}$ of binary (respectively, extended binary) Hamming codes of length $n=2^m-1$ (respectively, $2^m$), where $m=2u$. In the usual way, i.e., as coset graphs, infinite families of embedded distance-regular coset graphs of diameter $D$ equal to $3$ or $4$ are constructed. In some cases, the constructed codes are also completely transitive codes and the corresponding coset graphs are distance-transitive