Connections between Linear Complementary Dual Codes, Permanents and Geometry

Binary linear complementary dual codes

Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. We study binary linear complementary dual [n, k] codes with the largest minimum weight among all binary linear complementary dual [n, k] codes. We characterize binary linear complementary dual codes with the largest minimum weight for small dimensions. A complete ...

On linear complementary-dual multinegacirculant codes

Linear codes with complementary-duals (LCD) are linear codes that intersect with their dual trivially. Multinegacirculant codes of index 2 that are LCD are characterized algebraically and some good codes are found in this family. Exact enumeration is performed for indices 2 and 3, and for all indices t for a special case of the co-index by using their concatenated structure. Asymptotic existenc...

Connections between Linear Systems and Convolutional Codes

Connections between Linear Systems and Convolutional Codes

The article reviews different definitions for a convolutional code which can be found in the literature. The algebraic differences between the definitions are worked out in detail. It is shown that bi-infinite support systems are dual to finite-support systems under Pontryagin duality. In this duality the dual of a controllable system is observable and vice versa. Uncontrollability can occur on...

Complementary Dual Subfield Linear Codes Over Finite Fields

Two families of complementary codes over finite fields q are studied, where 2 = q r is square: i) Hermitian complementary dual linear codes, and ii) trace Hermitian complementary dual subfield linear codes. Necessary and sufficient conditions for a linear code (resp., a subfield linear code) to be Hermitian complementary dual (resp., trace Hermitian complementary dual) are determined. Construct...