Additive polycyclic codes over Fp^2 for any prime p

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Sarı M., Köroğlu M. E.

2nd International Conference on Engineering, Natural and Social Sciences, Konya, Türkiye, 4 - 06 Nisan 2023, ss.6-9

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Basıldığı Şehir: Konya
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.6-9
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

One of the most significant task in algebraic coding theory is to determine the structure of new

class of linear or nonlinear codes and to find codes having good parameters. In this study, for any prime

p , we define additive polycyclic codes over p2 F as a generalization of additive polycyclic codes over 4 F

studied in [5]. By making use of the polynomials over p F instead of p2 F , we determine the algebraic

structure of additive polycyclic codes over p2 F and present their generators completely. We also find the

cardinality for these codes. Moreover, under certain conditions, we show that the Euclidean duals of

additive polycyclic codes over p2 F are also additive polycyclic codes over p2 F . Finally, we illustrate

what we discuss in this study by offering some examples of additive polycyclic codes over 9 F that

enclose codewords as three times the number of the codewords of the optimal linear codes with the same

length and minimum distance.