We consider a code to be a subset of the vertex set of a Hamming graph. We examine elusive pairs, code-group pairs where the code is not determined by knowledge of its set of neighbours. We construct a new infinite family of elusive pairs, where the group in question acts transitively on the set of neighbours of the code. In our examples, we find that the alphabet size always divides the length...

This paper deals with propositional belief merging. The key problem in this setting is to define the beliefs/goals of a group of agents from a profile of bases, gathering the beliefs/goals of each member of the group. To this aim, a well-studied family of merging operators consists of distance-based ones: the models of the merged base are the closest interpretations to the given profile. Many o...

Let C be a code over q of length n and distance d = d(C): The (Hamming) distance distribution of the code is an (n + 1)-vector (A0 = 1; A1; : : : ; An); where Aw = Aw(C) := (]C) 1jf(x; x0) 2 C : d(x; x0) = wgj: Of course Aw = 0 if 1 w d 1: Let fCng be a family of binary linear codes of growing length n and let dn = d(Cn): G. Kalai and N. Linial [2] conjectured that for any such family the numbe...

We prove a version of the Ray-Chaudhuri–Wilson and Frankl–Wilson theorems for k-wise intersections and also generalize a classical code-theoretic result of Delsarte for k-wise Hamming distances. A set of code-words a; a; . . . ; ak of length n have k-wise Hamming-distance ‘; if there are exactly ‘ such coordinates, where not all of their coordinates coincide (alternatively, exactly n ‘ of their...

In this paper, we mainly consider quasi-cyclic (QC) codes over finite chain rings. We study module structures and trace representations of QC codes, which lead to some lower bounds on the minimum Hamming distance of QC codes. Moreover, we investigate the structural properties of 1-generator QC codes. Under some conditions, we discuss the enumeration of 1-generator QC codes and describe how to o...

A new high rate binary linear block code construction technique, named as Geometric Construction (GC) codes, was proposed recently [1]. It generates all the even full information rate (optimal) Hamming distance – 4 codes. In this paper, we have enhanced the construction of GC codes with respect to code rate and derived a code family of hamming distance-8 GC codes.

Background: In myocardial perfusion SPECT imaging, images are degraded by photon attenuation, the distance-dependent collimator, detector response and photons scatter. Filters greatly affect quality of nuclear medicine images Materials and Methods: A phantom simulating heart left ventricle was built. About 1mCi of 99mTc was injected into the phantom. Images were taken from this phantom. Some fi...

Linear regression side channel attack (LRA) used to be known as a robust attacking method as it makes use of independent bits leakage. This leakage assumption is more general than Hamming weight/ Hamming distance model used in correlation power attack (CPA). However, in practice, Hamming weight and Hamming distance model suit most devices well. In this paper, we restudy linear regression attack...