A new [47; 15; 16] linear binary block code and its weight spectrum is presented. The code is better than the previously known [47;15;15] code and it reaches the upper bound on code distance for the codeword length 47 and dimension 15.

In this paper we study the cyclic codes over Zm as being Zm-submodules of ZmG and we find their minimal generating sets. We also study the dual codes of cyclic codes and find their generators as being ideals in ZmG. Throughout this paper, we assume m = q, q is a prime number and (n, q) = 1.

For the block cipher RIJNDAEL with a block length of 128 bits group theoretic properties of the round functions are derived. Especially it is shown that these round functions generate the alternating group.

A Z2-triple cyclic code of block length (r,s, t) is a binary code of length r + s+ t such that the code is partitioned into three parts of lengths r, s and t such that each of the three parts is invariant under the cyclic shifts of the coordinates. Such a code can be viewed as Z2[x]-submodules of Z2[x] 〈xr−1〉 × Z2[x] 〈xs−1〉 × Z2[x] 〈xt−1〉 , in polynomial representation. In this paper, we determ...

In this paper, bounds are derived on the minimum homogeneous distance of the image of a linear block code over the Galois ring GR(p, m), with respect to any basis of GR(p, m). These bounds depend on the parameters of GR(p, m), the minimum Hamming distance of the block code, and the average value of the homogeneous weight applied on the base ring Zpr . Examples are given of Galois ring codes tha...

The minimum distance graph of an extended Preparata code P (m) has vertices corresponding to codewords and edges corresponding to pairs of codewords that are distance 6 apart. The clique structure of this graph is investigated and it is established that the minimum distance graphs of two extended Preparata codes are isomorphic if and only if the codes are equivalent.