In this work, we investigate linear codes over the ring $${\mathbb{F}_2+u\mathbb{F}_2+v\mathbb{F}_2+uv\mathbb{F}_2}$$ . We first analyze the structure of the ring and then define linear codes over this ring which turns out to be a ring that is not finite chain or principal ideal contrary to the rings that have ...
In this work, quadratic double and quadratic bordered double circulant constructions are applied to F 4 + u F 4 as well as to F 4 , and as a result, extremal binary self-dual codes of length 56 and 64 are obtained. The binary extension theorems as well ...
Let $$\mathbb {F}_q$$Fq be a finite field of cardinality $$q$$q, $$l$$l a prime number and $$\mathbb {F}_{q^l}$$Fql an extension field of $$\mathbb {F}_q$$Fq with degree $$l$$l. The structure and canonical form decompositions of semisimple multivariable ...
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