Additive skew G-codes over finite fields
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CitationDougherty S.T., Korban A., Şahinkaya S., Ustun D.(2023). Additive skew G-codes over finite fields. Applicable Algebra in Engineering, Communications and Computing, 34 (3), 423 - 442. DOI: 10.1007/s00200-021-00515-6
We define additive skew G-codes over finite fields and discuss several dualities attached to these codes. We examine the properties of self-dual skew G-codes and in particular we show that the dual, under any duality, of an additive skew G-code is also an additive skew G-code. Additionally, we propose a matrix construction for additive skew G-codes and use it to construct several examples of extremal self-dual additive skew G-codes over the finite field F4. Such codes have a strong connection to quantum error correcting codes.