From cosets of binary Hamming codes we construct diameter perfect constantweight ternary codes with weight n − 1 (where n is the code length) and distances 3 and 5. The class of distance 5 codes has parameters unknown before.

[x]i = (x (0) 0 , . . . , x (k−1) 0 , x (0) 1 , . . . , x (k−1) 1 , . . . , x (0) i−1, . . . , x (k−1) i−1 ), [y]i = (y (0) 0 , . . . , y (n−1) 0 , y (0) 1 , . . . , y (n−1) 1 , . . . , y (0) i−1, . . . , y (n−1) i−1 ). The column distance function (CDF) di is the minimum Hamming distance between all pairs of output sequences truncated at length i given that the input sequences differ in the fi...

Let [n; k; d]q-codes be linear codes of length n, dimension k and minimum Hamming distance d over GF(q). In this paper, 32 new codes over GF(5) are constructed and the nonexistence of 51 codes is proved. c © 2003 Elsevier B.V. All rights reserved.

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 1975 Ahlswede and Katona posed the following average distance problem ([1], page 10): For every cardinality a ∈ {1, . . . , 2} determine subsets A of {0, 1} with #A = a , which have minimal average inner Hamming distance. Recently Althöfer and Sillke gave an exact solution of this problem for the central value a = 2 . Here we present nearly optimal solutions for a = 2 with 0 < λ < 1 : Asympt...

In this correspondence, we study optimal self-dual codes and Type IV self-dual codes over the ring F2 + vF2 of order 4. We give improved upper bounds on minimum Hamming and Lee weights for such codes. Using the bounds, we determine the highest minimum Hamming and Lee weights for such codes of lengths up to 30. We also construct optimal self-dual codes and Type IV self-dual codes.

We derive the Varshamov{Gilbert and Hamming bounds for packings of spheres (codes) in the Grassmann manifolds over R and C. The distance between two k-planes is deened as (p; q) = (sin 2 1 + +sin 2 k) 1=2 , where i ; 1 i k, are the principal angles between p and q.

Let ( ) be the maximum possible minimum Hamming distance of a ternary [ ]-code for given values of and . We describe a package for code extension and use this to prove some new exact values of ( ). Moreover, we classify the ternary [ ( )]-codes for some values of and .

We first introduce the Hamming distance between two strings. Then, we apply this concept to the representations of whole numbers in base n for all positive integers n > 2. We claim that a simple formula exists for the sum of all Hamming distances between pairs of consecutive integers from 1 to m, which we will derive. We also state and prove other interesting results concerning the aforemention...