The support of an [n, k] linear code C over a finite field Fq is the set of all coordinate positions such that at least one codeword has a nonzero entry in each of these coordinate position. The rth generalized Hamming weight dr (C), 1 r k, of C is defined as the minimum of the cardinalities of the supports of all [n, r] subcodes of C. The sequence (d1(C), d2(C), . . . , dk(C)) is called the Ha...

In this paper, starting with a family of convolutional codes, we construct a new convolutional code and we introduce also necessary and sufficient conditions in order that the new convolutional code is MDS.

In this paper, we give algorithms and methods of construction of self-dual codes over finite fields using orthogonal matrices. Randomization in the orthogonal group, and code extension are the main tools. Some optimal, almost MDS, and MDS self-dual codes over both small and large prime fields are constructed.

A code C ⊆ F is a collection of M codewords where n elements (from the finite field F) in each of the codewords are referred to as code blocks. Assuming that F is a degree ` extension of a smaller field B, the code blocks are treated as `-length vectors over the base field B. Equivalently, the code is said to have the sub-packetization level `. This paper addresses the problem of constructing M...

Let q denote the finite field GF (q) and let b be a positive integer. MDS codes over the symbol alphabet b q are considered that are linear over q and have sparse (“low-density”) parity-check and generator matrices over q that are systematic over bq . Lower bounds are presented on the number of nonzero elements in any systematic parity-check or generator matrix of an q-linear MDS code over bq, ...

Let R be a finite chain ring (e.g. a Galois ring), K its residue field and C a linear code over R. We prove that d(C), the Hamming distance of C, is d((C : α)), where (C : α) is a submodule quotient, α is a certain element of R and denotes the canonical projection to K. These two codes also have the same set of minimal codeword supports. We explicitly construct a generator matrix/polynomial of ...

Let R be a finite chain ring (e.g. a Galois ring), K its residue field and C a linear code over R. We prove that d(C), the Hamming distance of C, is d((C : α)), where (C : α) is a submodule quotient, α is a certain element of R and denotes the canonical projection to K. These two codes also have the same set of minimal codeword supports. We explicitly construct a generator matrix/polynomial of ...

Abstmct We reveal an equivalence relation between the construction of a new class of low density MDS array codes, that we call B-Code, and a combinatorial problem known as perfect one-factorization of complete graphs. We use known perfect one-factors of complete graphs to create constructions and decoding algorithms for both B-Code and its dual code. B-Code and its dual are optimal in the sense...

This paper describes techniques used to leverage high performance legacy codes as CORBA components to a distributed problem solving environment. It first briefly introduces the software architecture adopted by the environment. Then it presents a CORBA oriented wrapper generator (COWG) which can be used to automatically wrap high performance legacy codes as CORBA components. Two legacy codes hav...