230 research outputs found
Generator polynomial matrices of the Galois hulls of multi-twisted codes
In this study, we consider the Euclidean and Galois hulls of multi-twisted
(MT) codes over a finite field of characteristic . Let
be a generator polynomial matrix (GPM) of a MT code .
For any , the -Galois hull of , denoted by
, is the intersection of with
its -Galois dual. The main result in this paper is that a GPM for
has been obtained from . We
start by associating a linear code with .
We show that is quasi-cyclic. In addition, we prove
that the dimension of is the difference
between the dimension of and that of .
Thus the determinantal divisors are used to derive a formula for the dimension
of . Finally, we deduce a GPM formula for
. In particular, we handle the cases of
-Galois self-orthogonal and linear complementary dual MT codes; we
establish equivalent conditions that characterize these cases. Equivalent
results can be deduced immediately for the classes of cyclic, constacyclic,
quasi-cyclic, generalized quasi-cyclic, and quasi-twisted codes, because they
are all special cases of MT codes. Some numerical examples, containing optimal
and maximum distance separable codes, are used to illustrate the theoretical
results
Finite nonassociative algebras obtained from skew polynomials and possible applications to (f, σ, δ)-codes
Let S be a unital ring, S[t; σ, δ] a skew polynomial ring where σ is an injective endomorphism and δ a left σ -derivation, and suppose f ε S[t; σ, δ] has degree m and an invertible leading coefficient. Using right division by f to define the multiplication, we obtain unital nonassociative algebras Sf on the set of skew polynomials in S[t; σ, δ] of degree less than m. We study the structure of these algebras. When S is a Galois ring and f base irreducible, these algebras yield families of finite unital nonassociative rings A, whose set of (left or right) zero divisors has the form pA for some prime p. For reducible f, the Sf can be employed both to design linear (f, σ, δ)-codes over unital rings and to study their behaviour
NASA Tech Briefs, December 1989
Topics include: Electronic Components and Circuits. Electronic Systems, Physical Sciences, Materials, Computer Programs, Mechanics, Machinery, Fabrication Technology, Mathematics and Information Sciences, and Life Sciences
Data systems elements technology assessment and system specifications, issue no. 2
The ability to satisfy the objectives of future NASA Office of Applications programs is dependent on technology advances in a number of areas of data systems. The hardware and software technology of end-to-end systems (data processing elements through ground processing, dissemination, and presentation) are examined in terms of state of the art, trends, and projected developments in the 1980 to 1985 timeframe. Capability is considered in terms of elements that are either commercially available or that can be implemented from commercially available components with minimal development
Aeronautical Engineering, a continuing bibliography with indexes
This bibliography lists 546 reports, articles and other documents introduced into the NASA scientific and technical information system in October 1984
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