For an error-correcting code and a distance bound, the list decoding problem is to compute all the codewords within the given distance to a received message. The bounded distance decoding problem, on the other hand, is to find one codeword if there exists one or more codewords within the given distance, or to output the empty set if there does not. Obviously the bounded distance decoding proble...

In this note, we show how the determinant of the q-distance matrix Dq(T ) of a weighted directed graph G can be expressed in terms of the corresponding determinants for the blocks of G, and thus generalize the results obtained by Graham et al. [R.L. Graham, A.J. Hoffman and H. Hosoya, On the distance matrix of a directed graph, J. Graph Theory 1 (1977) 85–88]. Further, by means of the result, w...

Perfect codes and minimal distance of a code have great importance in the study of theory of codes. The perfect codes are classified generally and in particular for the Lee metric. However, there are very few perfect codes in the Lee metric. The Lee metric has nice properties because of its definition over the ring of integers residue modulo q. It is conjectured that there are no perfect codes ...

In [GIJ01a, GIJ01b] we described how to use q-grams in an RDBMS to perform approximate string joins. We also showed how to implement the approximate join using plain SQL queries. Specifically, we described three filters, count filter, position filter, and length filter, which can be used to execute efficiently the approximate join. The intuition behind the count filter was that strings that are...

This paper is devoted to the study of linear codes with complementary-duals (LCD) arising from negacyclic codes over finite fields Fq, where q is an odd prime power. We obtain two classes of MDS negacyclic LCD codes of length n| q−1 2 , n| q+1 2 and a class of negacyclic LCD codes of length n = q+1. Also, we drive some parameters of Hermitian negacyclic LCD codes over Fq2 of length n = q − 1 an...

The distance distribution of a code is the vector whose ith entry number pairs codewords with i. We investigate structure for cyclic orbit codes, which are subspace codes generated by action $${\mathbb {F}}_{q^n}^*$$ on an {F}}_q$$ -subspace U {F}}_{q^n}$$ . Note that Singer cycle in general linear group all -automorphisms show full-length maximal possible depends only $$q,\,n$$ , and dimension...

We calculate the NRQCD matrix elements for the decays of the lowest-lying Sand P-wave states of charmonium and bottomonium in quenched lattice QCD. We also compute the one-loop relations between the lattice and continuum matrix elements. Heavy-quarkonium systems are nonrelativistic. In the CM frame, the average quark velocity v satisfies v 2 ≪ 1, where v 2 ≈ 0.3 for charmonium, and v 2 ≈ 0.1 fo...

We appreciate the comments from the associate editor and all reviewers in this paper. We have made necessary experiments and modifications to cope with all the comments. The basic notations for different fonts are: Bold face fonts are from reviewers' original comments. Italic face fonts are the modified/added texts in the paper. Plain fonts are our answers to reviewers' comments. Q1: There is a...

A parity-check matrix for a q -ary repeated-root cyclic code is derived using the Hasse derivative. Then the min imum distance of a q-ary repeated-root cyclic code C is expressecin terms of the min imum distance of a certain simple-root cyclic code C that is determined by C. With the help of this result, several binary repeated-root cyclic codes of lengths up to n = 62 are shown to contain the ...