A generalization of multi-twisted codes over finite fields, their Galois duals and Type II codes

Chauhan, Varsha; Sharma, Anuradha

doi:10.1007/s12190-021-01574-1

J. Appl. Math. Comput.

2021

DOI: 10.1007/s12190-021-01574-1

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A generalization of multi-twisted codes over finite fields, their Galois duals and Type II codes

Varsha Chauhan

Anuradha Sharma

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2023

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Two-sided Galois duals of multi-twisted codes

ElDin

2023

J. Appl. Math. Comput.

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Galois duals of Multi-twisted (MT) codes are considered in this study. We describe a MT code $$\mathcal {C}$$ C as a module over a principal ideal domain. Hence, $$\mathcal {C}$$ C has a generator polynomial matrix (GPM) $$\textbf{G}$$ G that satisfies an identical equation. We prove a GPM formula for the Euclidean dual $$\mathcal {C}^\perp $$ C ⊥ using the identical equation of the Hermite normal form of $$\textbf{G}$$ G . Next, we aim to replace the Euclidean dual with the Galois dual. The Galois inner product is an asymmetric form, so we distinguish between the right and left Galois duals. We show that the right and left Galois duals of a MT code are MT as well but with possibly different shift constants. Some interconnected identities for the right and left Galois duals of a linear code are established and we also introduce the two-sided Galois dual. We use a condition that makes the two-sided Galois dual of a MT code MT, then we describe its GPM. Two special cases are also studied, one when the right and left Galois duals trivially intersect and the other when they coincide. A necessary and sufficient condition is established for the equality of the right and left Galois duals of any linear code.

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Two-sided Galois duals of multi-twisted codes

ElDin

2023

J. Appl. Math. Comput.

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show abstract

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A generalization of multi-twisted codes over finite fields, their Galois duals and Type II codes

Cited by 1 publication

References 18 publications

Two-sided Galois duals of multi-twisted codes

Two-sided Galois duals of multi-twisted codes

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