On affine variety codes from the Klein quartic

Geil, Olav; ÖZBUDAK, FERRUH

doi:10.1007/s12095-018-0285-6

On affine variety codes from the Klein quartic

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, cilt.11, sa.2, ss.237-257, 2019 (SCI-Expanded)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 11 Sayı: 2
Basım Tarihi: 2019
Doi Numarası: 10.1007/s12095-018-0285-6
Dergi Adı: CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Sayfa Sayıları: ss.237-257
Anahtar Kelimeler: Affine variety codes, Grobner basis, Klein curve
Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

We study a family of primary affine variety codes defined from the Klein quartic. The duals of these codes have previously been treated in Kolluru et al., (Appl. Algebra Engrg. Comm. Comput. 10(6):433-464, 2000, Ex. 3.2). Among the codes that we construct almost all have parameters as good as the best known codes according to Grassl (2007) and in the remaining few cases the parameters are almost as good. To establish the code parameters we apply the footprint bound (Geil and HOholdt, IEEE Trans. Inform. Theory 46(2), 635-641, 2000 and HOholdt 1998) from Grobner basis theory and for this purpose we develop a new method where we inspired by Buchberger's algorithm perform a series of symbolic computations.