Newton Complementary Duals of -Ideals

Derivations Into N-th Duals of Ideals of Banach Algebras

Linear codes with complementary duals

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...

Explicit MDS Codes with Complementary Duals

In 1964, Massey introduced a class of codes with complementary duals which are called Linear Complimentary Dual (LCD for short) codes. He showed that LCD codes have applications in communication system, side-channel attack (SCA) and so on. LCD codes have been extensively studied in literature. On the other hand, MDS codes form an optimal family of classical codes which have wide applications in...

Derivations into Duals of Closed Ideals of Banach Algebras

Let A be a Banach algebra. We study those closed ideals I of A for which the first cohomology group of A with coefficients in I is trivial; i.e. H(A, I) = {0}. We investigate such closed ideals when A is weakly amenable or biflat. Also we give some hereditary properties of ideal amenability.

Finite-dimensional Left Ideals in the Duals of Introverted Spaces

We use representations of a Banach algebra A to completely characterize all finite-dimensional left ideals in the dual of introverted subspaces of A∗ and in particular in the double dual A∗∗. We give sufficient conditions under which such ideals always exist and are direct sums of one-dimensional left ideals.