We study 1-perfect codes in Doob graphsD(m,n). We show that such codes that are linear over GR(4) exist if and only if n = (4γ+δ−1)/3 andm = (4γ+2δ−4γ+δ)/6 for some integers γ ≥ 0 and δ > 0. We also prove necessary conditions on (m,n) for 1-perfect codes that are linear over Z4 (we call such codes additive) to exist in D(m,n) graphs; for some of these parameters, we show the existence of codes....

Within the framework of exact renormalization group flow equations, a scale-dependent transformation of the field variables provides for a continuous translation of UV to IR degrees of freedom. Using the gauged NJL model as an example, this translation results in a construction of partial bosonization at all scales. A fixedpoint structure arises which makes it possible to distinguish between fu...

In this lecture I want delve a bit more deeply into the problem of comparing performance of various tests. Among other things I will try to provide an exposition of Chernoff’s (1952) result employed in Lars Hansen’s talks here several years ago. The lecture is based on van der Vaart (1998, Chapter 14). Consider the problem of testing H0 : θ ∈ Θ0 vs H1 : θ ∈ Θ1, using a test statistic Tn that re...

In this paper, we describe a procedure for constructing q– ary [N, 3, N−2]–MDS codes, of length N ≤ q+1 (for q odd) or N ≤ q+2 (for q even), using a set of non–degenerate Hermitian forms in PG(2, q).

A new class of codes over GF(q’) that meet the Griesmer bound are constructed in a simple way from the Solomon and Stiffler codes over GF(q). The new codes are, in general, not equivalent to the Solomon and Stiffler codes whenever I > 1.

A new class of full diversity space-time codes is proposed that leads to a significantly smaller Peak-to-Mean Envelope Power Ratio (PMEPR) compared to the recently invented Diagonal Algebraic SpaceTime (DAST) and Threaded Algebraic Space-Time (TAST) codes. Moreover, the proposed “Low PMEPR Space-Time” (LPST) codes exhibit identical performance and decoding complexity compared to the TAST codes....

Some features and predictions of a recently proposed model based on diquark-antidiquark bound states are illustrated. Its ability in accomodating newly discovered charmed resonances around 4 GeV is discussed.

In this paper we consider the existence of nontrivial perfect codes in the Johnson graph J(n, w). We present combinatorial and number theory techniques to provide necessary conditions for existence of such codes and reduce the range of parameters in which 1-perfect and 2-perfect codes may exist.

We will construct an MDS(= the most distance separable) code C which admits a decomposition C = ⊕iCi such that every factor is still MDS. An effective way of decoding will be also discussed.