Fast Encoding of AG Codes Over CabCurves

Autor: Johan Rosenkilde, Grigory Solomatov, Peter Beelen

Publikováno v: Beelen, P, Rosenkilde, J & Solomatov, G 2021, ' Fast Encoding of AG Codes over C ab Curves ', IEEE Transactions on Information Theory, vol. 67, no. 3, pp. 1641-1655 . https://doi.org/10.1109/TIT.2020.3042248

We investigate algorithms for encoding of one-point algebraic geometry (AG) codes over certain plane curves called $C_{ab}$ curves, as well as algorithms for inverting the encoding map, which we call “unencoding”. Some $C_{ab}$ curves have many p

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4ec26668820d0e8c435be0400b417909
https://doi.org/10.1109/tit.2020.3042248

Twisted Hermitian Codes

Autor: Zoe Nelson, Rutuja Kshirsagar, Austin Allen, Bethany Matsick, Gretchen L. Matthews, Olivia Fiol, Keller Blackwell

Publikováno v: Mathematics, Vol 9, Iss 40, p 40 (2021)
Mathematics
Volume 9
Issue 1

We define a family of codes called twisted Hermitian codes, which are based on Hermitian codes and inspired by the twisted Reed&ndash
Solomon codes described by Beelen, Puchinger, and Nielsen. We demonstrate that these new codes can have high-di

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::568d7ef2a7958df5ccaf96161eee9d68
https://www.mdpi.com/2227-7390/9/1/40

An Algorithmic Approach to Entanglement-Assisted Quantum Error-Correcting Codes from the Hermitian Curve

Autor: Christensen, Ren�� B��dker, Munuera, Carlos, Pereira, Francisco Revson F., Ruano, Diego

Publikováno v: Christensen, R B, Munuera, C, Pereira, F R F & Ruano, D 2023, ' An algorithmic approach to entanglement-assisted quantum error-correcting codes from the Hermitian curve ', Advances in Mathematics of Communication, vol. 17, no. 1, pp. 78-97 . https://doi.org/10.3934/amc.2021072

We study entanglement-assisted quantum error-correcting codes (EAQECCs) arising from classical one-point algebraic geometry codes from the Hermitian curve with respect to the Hermitian inner product. Their only unknown parameter is $c$, the number of

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dd833aa19058d48248db50fbf4c488f6

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