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Segre's theorem on ovals in projective spaces is an ingenious result from the mid-twentieth century which requires surprisingly little background to prove. This note, suitable for undergraduates with experience of linear and abstract algebra, provide
Externí odkaz:
http://arxiv.org/abs/2301.05171
In this paper, we give a new method for constructing LCD codes. We employ group rings and a well known map that sends group ring elements to a subring of the $n \times n$ matrices to obtain LCD codes. Our construction method guarantees that our LCD c
Externí odkaz:
http://arxiv.org/abs/2108.05056
In this work, we study codes generated by elements that come from group matrix rings. We present a matrix construction which we use to generate codes in two different ambient spaces: the matrix ring $M_k(R)$ and the ring $R,$ where $R$ is the commuta
Externí odkaz:
http://arxiv.org/abs/2102.00475
In this work, we define composite matrices which are derived from group rings. We extend the idea of G-codes to composite G-codes. We show that these codes are ideals in a group ring, where the ring is a finite commutative Frobenius ring and G is an
Externí odkaz:
http://arxiv.org/abs/2002.11614
A subset of a vector space $\mathbb{F}_q^n$ is $K$-additive if it is a linear space over the subfield $K\subseteq \mathbb{F}_q$. Let $q=p^e$, $p$ prime, and $e>1$. Bounds on the rank and dimension of the kernel of generalised Hadamard (GH) codes whic
Externí odkaz:
http://arxiv.org/abs/2001.11609
Akademický článek
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Linear complementary dual codes were defined by Massey in 1992, and were used to give an optimum linear coding solution for the two user binary adder channel. In this paper, we define the analog of LCD codes over fields in the ambient space with mixe
Externí odkaz:
http://arxiv.org/abs/1903.07886
Akademický článek
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Publikováno v:
In Finite Fields and Their Applications October 2022 83
