An efficient coset based symbol-by-symbol soft-in/soft-out APP decoding algorithm is presented for the Golay code. Its application in the iterative decoding of concatenated Golay codes is examined.

An efficient coset based symbol-by-symbol soft-in/soft-out APP decoding algorithm is presented for the Golay code. Its application in the iterative decoding of concatenated Golay codes is examined.

The origin of all 4-phase Golay sequences and Golay sequence pairs of even length at most 26 is explained. The principal techniques are the three-stage construction of Fiedler, Jedwab and Parker [FJP08] involving multi-dimensional Golay arrays, and a “sum-difference” construction that modifies a result due to Eliahou, Kervaire and Saffari [EKS91]. The existence of 4-phase seed pairs of lengths ...

In this paper, we propose new binary complementary codes, which compress a pulse to a width of several sub-pulses, and survey all combinations of the binary complementary codes with several code lengths. We are able to find a large number of binary complementary codes and complete complementary codes. Furthermore, we show that longer such complementary codes can be acquired using the expansion ...

A pair of quasi-de nite linear functionals fu0; u1g on the set of polynomials is called a coherent pair if their corresponding sequences of monic orthogonal polynomials fPng and fTng satisfy a relation Tn = P 0 n+1 n+ 1 nP 0 n n ; n 1; with n non-zero constants. We prove that if fu0; u1g is a coherent pair, then at least one of the functionals has to be classical, i.e. Hermite, Laguerre, Jacobi...

‎we introduce a generalization of the notion of‎ depth of an ideal on a module by applying the concept of‎ local cohomology modules with respect to a pair‎ ‎of ideals‎. ‎we also introduce the concept of $(i,j)$-cohen--macaulay modules as a generalization of concept of cohen--macaulay modules‎. ‎these kind of modules are different from cohen--macaulay modules‎, as an example shows‎. ‎also an art...

We study the structure of resultants of two homogeneous partially composed polynomials. By two homogeneous partially composed polynomials we mean a pair of polynomials of which one does not have any given composition structure and the other one is obtained by composing a bivariate homogeneous polynomial with two bivariate homogeneous polynomials. The main contributions are two equivalent formul...

Suppose G is a connected, k-regular graph such that Spec…G† ˆ Spec…G† where G is a distance-regular graph of diameter d with parameters a1 ˆ a2 ˆ ˆ adÿ1 ˆ 0 and ad > 0; i.e., a generalized odd graph, we show that G must be distance-regular with the same intersection array as that of G in terms of the notion of Ho ̈man Polynomials. Furthermore, G is isomorphic to G if G is one of the odd polygon ...

In this paper, an algebraic decoding method is proposed for the quadratic residue codes that utilize the Berlekamp-Massey algorithm. By a modification of the technique developed by He et al., one can express the unknown syndromes as functions of the known syndromes. The unknown syndromes are determined by an efficient algorithm also developed in this paper. With the appearance of unknown syndro...