A new bound on the minimum distance of q-ary cyclic codes is proposed. It is based on the description by another cyclic code with small minimum distance. The connection to the BCH bound and the Hartmann–Tzeng (HT) bound is formulated explicitly. We show that for many cases our approach improves the HT bound. Furthermore, we refine our bound for several families of cyclic codes. We define syndro...

Recently, a new parameter of a code, referred to as the remoteness, has been introduced.This parameter can be viewed as a dual to the covering radius. It is exactly determined for the cyclic and dihedral groups. In this paper, we consider the group $U_{6n}$ as a subgroup of $S_{2n+3}$ and obtain its remoteness.  We show that the remoteness of the permutation code $U_{6n}$ is $2n+2$.  Moreover, ...

We disprove a conjecture of Bultena and Ruskey [1], that all trees which are cyclic graphs of cyclic Gray codes have diameter 2 or 4, by producing codes whose cyclic graphs are trees of arbitrarily large diameter. We answer affirmatively two other questions from [1], showing that strongly Pn × Pncompatible codes exist and that it is possible for a cyclic code to induce a cyclic digraph with no ...

Instead of a random interleaver, an algebraic interleaver interconnecting two simple convolutional codes with feedback encoders forms an algebraic quasi-cyclic code. An (nC , k) convolutional code in tailbiting form becomes a quasi-cyclic (QC) linear code of length LnC for some L = Mn. Interleavers with a period M connect two such codes to produce a QC turbo code. The QC turbo codes check equat...

An n-bit (cyclic) Gray code is a (cyclic) sequence of all n-bit strings such that consecutive strings differ in a single bit. We describe an algorithm which for every positive integer n constructs an n-bit cyclic Gray code whose graph of transitions is the d-dimensional hypercube Qd if n = 2, or a subgraph of Qd if 2 d−1 < n < 2. This allows to compress sequences that follow this code so that o...

I N THIS PAPER, a binary code is called a b-burst-correcting code if it can correct any single cyclic burst of length b, or less. If C is an [n, n r] b-burst-correcting code, then the syndromes corresponding to the different cyclic bursts of lengths I b should be nonzero and distinct. Since there are n2b-’ different cyclic bursts of length up to b, it follows that 2’ 2 1 + n2’-‘. Abramson [l] n...