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In this paper, we construct self-dual codes from a construction that involves 2x2 block circulant matrices, group rings and a reverse circulant matrix. We provide conditions whereby this construction can yield self-dual codes. We construct self-dual codes of various lengths over F2, F2 + uF2 and F4 + uF4. Using extensions, neighbours and neighbours of neighbours, we construct 32 new self-dual codes of length 68.
In this paper, we construct self-dual codes from a construction that involves both block circulant matrices and block quadratic residue circulant matrices. We provide conditions when this construction can yield self-dual codes. We construct self-dual
In the present paper we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free group and introduce three axioms for the corresponding defining relation
Using the Luthar--Passi method, we investigate the possible orders and partial augmentations of torsion units of the normalized unit group of integral group rings of Conway simple groups $Co_1$, $Co_2$ and $Co_3$.
The prime graph question asks whether the Gruenberg-Kegel graph of an integral group ring $mathbb Z G$ , i.e. the prime graph of the normalised unit group of $mathbb Z G$ coincides with that one of the group $G$. In this note we prove for finite grou
We study a bilinear multiplication rule on 2x2 matrices which is intermediate between the ordinary matrix product and the Hadamard matrix product, and we relate this to the hyperbolic motion group of the plane.