Atıf İçin Kopyala
Sarı M., Aydoğdu İ.
2^nd International Symposium on current developments in fundamental and applied mathematics sciences, Ankara, Türkiye, 14 - 17 Kasım 2023, ss.55
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Yayın Türü:
Bildiri / Özet Bildiri
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Basıldığı Şehir:
Ankara
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Basıldığı Ülke:
Türkiye
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Sayfa Sayıları:
ss.55
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Yıldız Teknik Üniversitesi Adresli:
Evet
Özet
Skew
cyclic codes are one of the important family of codes in coding theory which
are actually generalization of classical cyclic codes. In this work, we
introduce and study the algebraic structure of skew cyclic codes over the mixed
alphabet F_2^r * F_4^r where F_2 and F_4 are finite fields of
2 and 4 elements, respectively
with non-negative integers r and s. We first determine the
generator polynomials of F_2F_4-skew cyclic codes. Further, we relate skew cyclic codes over
F_2F_4 to binary linear codes
by defining a linear Gray map. We also investigate the duals of skew cyclic
codes over this mixed alphabet. We show that the dual of any F_2F_4-skew cyclic code is another F_2F_4-skew cyclic code. As an application of our work, we provide
several examples of F_2F_4-skew cyclic codes whose binary images have optimal
parameters under the Gray mapping. We also consider the quantum codes over F_2^r * F_4^r. By using the well-known construction method of quantum
codes (CSS), we obtain examples of quantum codes with good parameters.
Keywords: Skew
cyclic codes, F_2F_4, optimal codes, generator polynomials.