No Access

CYCLIC CODES THROUGH , WITH AND b = a+1, AND ENCODING

TARIQ SHAH

Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan

Search for more papers by this author

and

ANTONIO APARECIDO DE ANDRADE

Department of Mathematics, São Paulo State University at São José do Rio Preto – SP, Brazil

Search for more papers by this author

https://doi.org/10.1142/S1793830912500590Cited by:4 (Source: Crossref)

Abstract

Let B[X; S] be a monoid ring with any fixed finite unitary commutative ring B and is the monoid S such that b = a + 1, where a is any positive integer. In this paper we constructed cyclic codes, BCH codes, alternant codes, Goppa codes, Srivastava codes through monoid ring . For a = 1, almost all the results contained in [16] stands as a very particular case of this study.

Keywords:

AMSC: 11T71, 94A15, 14G50

References

A. A. Andrade and R. Palazzo Jr., Tend. Mat. Apl. Comput. 6(2), 207 (2005). Crossref, Google Scholar
A. A. Andrade, T. Shah and A. Khan, Int. J. Appl. Math. 23(3), 515 (2010). Google Scholar
N. Bourbaki , Eléments de Mathématiques , 2nd edn. , Livre II: Algèbre, 2ème edn ( Hermann , Paris, France , 1964 ) . Google Scholar
J. Cazaran and A. V. Kelarev , Arch. Math. 69 , 479 ( 1997 ) . Crossref, Google Scholar
J. Cazaran and A. V. Kelarev, Acta Math. Univ. Comenianae 68(1), 77 (1999). Google Scholar
J. Cazaran et al. , Simgroup Forum 73 , 317 ( 2006 ) . Crossref, Google Scholar
R. Gilmer , Multiplicative Ideal Theory ( Marcel Dekker , New York , 1972 ) . Google Scholar
R. Gilmer , Commutative Semigroup Rings ( University Chicago Press , Chicago and London , 1984 ) . Google Scholar
R. Gilmer and T. Parker, Michigan Math. J. 21(1), 65 (1974). Crossref, Google Scholar
H. J. Helgret, IEEE Trans. Inform. Theory 18(2), 292 (1972). Crossref, Google Scholar
A. V. Kelarev , Ring Constructions and Applications ( World Scientific , River Edge, New York , 2002 ) . Google Scholar
A. V. Kelarev , J. Discrete Algorithms 5 , 553 ( 2007 ) . Crossref, Google Scholar
A. V. Kelarev, Fund. Inform. 84(1), 51 (2008). Google Scholar
B. R. McDonlad , Finite Rings with Identity ( Marcel Dekker , New York , 1974 ) . Google Scholar
T. Shah, S. Farwa and R. S. Badar, Adv. Algebra 3(1), 43 (2010). Google Scholar
T. Shah, A. Khan and A. A. Andrade, Comput. Appl. Math. 30(2), 349 (2011). Crossref, Google Scholar