Conditions on the existence of self-dual θ-codes defined over a finite field IFq are studied for θ automorphism of IFq. When q ≡ 1 (mod 4) it is proven that there always exists a self-dual θ-code in any dimension and that self-dual θ-codes of a given dimension are either all θ-cyclic or all θ-negacyclic. When q ≡ 3 (mod 4), there does not exist a selfdual θ-cyclic code and a necessary and suffi...

We obtain low complexity tail-biting trellises for some extremal self-dual codes for various lengths and fields such as the [12,6,6] ternary Golay code and a [24,12,8] Hermitian self-dual code over GF(4). These codes are obtained from a particular family of cyclic Tanner graphs called necklace factor graphs.

In this paper from q-ary perfect codes new completely regular q-ary codes are constructed. In particular, two new ternary completely regular codes are obtained from ternary Golay [11, 6, 5] code. The first [11, 5, 6] code with covering radius ρ = 4 coincides with the dual Golay code and its intersection array is (22, 20, 18, 2, 1; 1, 2, 9, 20, 22) . The second [10, 5, 5] code, with covering rad...

It is shown that the minimal distance d of a binary self-dual code of length n ≥ 74 is at most2 [ (n + 6 )/10 ]. This bound is a consequence of some new conditions on the weight enumerator ofa self-dual code obtained by considering a particular translate of the code called its ‘‘shadow’’.These conditions also enable us to find the highest possible minimal distance of a self-dual...

We show that the state complexity profile of a convolutional code is the same as that of the reciprocal of the dual code of in case that minimal encoders for both codes are used. Then, we propose an optimum permutation for any given ( 1) binary convolutional code that will yield an equivalent code with the lowest state complexity. With this permutation, we are able to find many ( 1) binary conv...

In this paper, we study the linear codes over the commutative ring R = Z4 + vZ4, where v2 = v. We define the Gray weight of the elements of R and give a Gray map from Rn to Z2n 4 , which lead to the MacWillams identity of the linear code over R. Some useful results on self-dual code over R are given. Furthermore, the relationship between some complex unimodular lattices and Hermitian self-dual ...

A linear code with a complementary dual (or an LCD code) is defined to be a linear code C whose dual code C⊥ satisfies C ∩ C⊥ = {0}. The algebraic characterization of LCD codes is given, and it is shown that asymptotically good LCD codes exist. LCD codes are shown to provide an optimum linear coding solution for the two-user binary adder channel. The nearest-neighbor (or maximum-likelihood) dec...

An [n, k] code C is said to be locally recoverable in the presence of a single erasure, and with locality parameter r, if each of the n code symbols of C can be recovered by accessing at most r other code symbols. An [n, k] code is said to be a locally recoverable code with sequential recovery from t erasures, if for any set of s ≤ t erasures, there is an s-step sequential recovery process, in ...

Conway and Sloane have previously given an upper bound on the minimum distance of a singly-even self-dual binary code, using the concept of the shadow of a self-dual code. We improve their bound, finding that the minimum distance of a selfdual binary code of length n is at most 4bn=24c+4, except when nmod24 = 22 , when the bound is 4bn=24c + 6. We also show that a code of length a multiple of 2...

We develop a Tanner graph (TG) construction for an Abelian group block code with arbitrary alphabets at different coordinates, an important application of which is the representation of the label code of a lattice. The construction is based on the modular linear constraints imposed on the code symbols by a set of generators for the dual code . As a necessary step toward the construction of a TG...