nach oben

Designs, Codes and Cryptography

Erschienen in:

01.01.2015

On cyclic codes over the ring \(\mathbb Z _p[u]/\langle u^k\rangle \)

verfasst von: Abhay Kumar Singh, Pramod Kumar Kewat

Erschienen in: Designs, Codes and Cryptography | Ausgabe 1/2015

Einloggen, um Zugang zu erhalten

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

In this paper, we study cyclic codes over the ring \(\mathbb Z _p[u]/\langle u^k\rangle .\) We find a set of generators for these codes. We also study the rank and the Hamming distance of these codes.

Nächster Artikel Two series of equitable symbol weight codes meeting the Plotkin bound

Abualrub T., Oehmke R.H.: On the generators of \(Z_4\) cyclic codes of length \(2^e.\) IEEE Trans. Inf. Theory 49(9), 2126–2133 (2003).

Abualrub T., Siap I.: Cyclic codes over the rings \(Z_2+uZ_2\) and \(Z_2+uZ_2+u^2Z_2.\) Des. Codes Cryptogr. 42(3), 273–287 (2007).

Abualrub T., Ghrayeb A., Oehmke R.H.: A mass formula and rank of \(Z_4\) cyclic codes of length \(2^e.\) IEEE Trans. Inf. Theory 50(12), 3306–3312 (2004).

Al-Ashker M., Hamoudeh M.: Cyclic codes over \(Z_2+uZ_2+u^2Z_2+\cdots +u^{k-1}Z_2.\) Turk. J. Math. 35(4), 737–749 (2011).

Blackford T.: Cyclic codes over \(Z_4\) of oddly even length. Discret. Appl. Math. 128(1), 27–46 (2003). International Workshop on Coding and Cryptography (WCC 2001) (Paris).

Bonnecaze A., Udaya P.: Cyclic codes and self-dual codes over \(F_2+uF_2.\) IEEE Trans. Inf. Theory 45(4), 1250–1255 (1999).

Calderbank A.R., Sloane N.J.A.: Modular and \(p\)-adic cyclic codes. Des. Codes Cryptogr. 6(1), 21–35 (1995).

Calderbank R.A., Rains E.M., Shor P.W., Sloane N.J.A.: Quantum error correction via codes over \({\rm GF}(4).\) IEEE Trans. Inf. Theory 44(4), 1369–1387 (1998).

Conway J.H., Sloane N.J.A.: Self-dual codes over the integers modulo 4. J. Comb. Theory A 62(1), 30–45 (1993).

10.

Dinh H.Q., Lopez-Permouth S.: Cyclic and negacyclic codes over finite chain rings. IEEE Trans. Inf. Theory 50(8), 1728–1744 (2004).

11.

Dougherty S.T., Shiromoto K.: Maximum distance codes over rings of order 4. IEEE Trans. Inf. Theory 47(1), 400–404 (2001).

12.

McDonald B.R.: Finite rings with identity. In: Pure and Applied Mathematics, vol. 28. Marcel Dekker, New York (1974).

13.

Pless V.S., Qian Z.: Cyclic codes and quadratic residue codes over \(Z_4.\) IEEE Trans. Inf. Theory 42(5), 1594–1600 (1996).

14.

van Lint J.H.: Repeated-root cyclic codes. IEEE Trans. Inf. Theory 37(2), 343–345 (1991).

Titel: On cyclic codes over the ring
verfasst von: Abhay Kumar Singh
Pramod Kumar Kewat
Publikationsdatum: 01.01.2015
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 1/2015
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-013-9843-2

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Weitere Artikel der Ausgabe 1/2015

ETRU: NTRU over the Eisenstein integers

Erratum to: Intersection of Hamming codes avoiding Hamming subcodes

A geometric protocol for cryptography with cards

Group divisible designs with block size four and group type

On the minimum number of points covered by a set of lines in

Two series of equitable symbol weight codes meeting the Plotkin bound