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On codes over $\mathcal{R}k,m$ and constructions for new binary self-dual codes

In: Mathematica Slovaca, vol. 66, no. 6
Nesibe Tufekci - Bahattin Yildiz

Details:

Year, pages: 2016, 1511 - 1526
Keywords:
extremal self-dual codes, Gray maps, codes over rings, MacWilliams identities
About article:
In this work, we study codes over the ring $\mathcal{R}k,m= \mathbb{F}2[u,v]/\langle uk,vm,uv-vu\rangle$, which is a family of Frobenius, characteristic $2$ extensions of the binary field. We introduce a distance and duality preserving Gray map from $\mathcal{R}k,m$ to $\mathbb{F}2km$ together with a Lee weight. After proving the MacWilliams identities for codes over $\mathcal{R}k,m$ for all the relevant weight enumerators, we construct many binary self-dual codes as the Gray images of self-dual codes over $\mathcal{R}k,m$. In addition to many extremal binary self-dual codes obtained in this way, including a new construction for the extended binary Golay code, we find 175 new Type I binary self-dual codes of parameters $[72,36,12]$ and 105 new Type II binary self-dual codes of parameter $[72,36,12]$.
How to cite:
ISO 690:
Tufekci, N., Yildiz, B. 2016. On codes over $\mathcal{R}k,m$ and constructions for new binary self-dual codes. In Mathematica Slovaca, vol. 66, no.6, pp. 1511-1526. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0240

APA:
Tufekci, N., Yildiz, B. (2016). On codes over $\mathcal{R}k,m$ and constructions for new binary self-dual codes. Mathematica Slovaca, 66(6), 1511-1526. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0240
About edition:
Published: 1. 12. 2016