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Generalized Gaussian Numbers Related to Linear Codes over Galois Rings

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Abstract (2. Language): 
In this paper, we define a family of Generalized Gaussian Numbers that gives the number of linear codes over Galois rings directly. Also, we study some of their properties and obtain some relations between them.
250-259

REFERENCES

References: 

[1] G. Calugareanu. The total number of subgroups of a finite Abelian group. Scientiae
Mathematicae Japonicae, 60:157-167, 2004.
[2] S. Delsarte. Fonctions de Möbius sur les groupes abeliens finis, Annals of Math. 49:600-
609, 1948.
[3] P.E. Djubjuk. On the number of subgroups of a finite abelian group, Izv. Akad. Nauk
SSSR Ser. Mat., 12:351-378, 1948.
[4] A.R. Hammons, P.V. Kumar, A.R. Calderbank, N.J.A. Sloane and P. Sole. The Z4-linearity
of Kerdock, Preparata, Goethals and related codes. IEEE Transactions on Information
Theory, 40:301-319, 1994.
[5] T. Honold and I. Landjev. Linear codes over finite chain rings, The Electronic Journal of
Combinatorics 7, 2000.
[6] W.C. Huffman. Decompositions and extremal type II codes over Z4. IEEE Trans. Inf.
Theory 44:800-809, 1998.
[7] M. Ozen and I. Siap. Codes over Galois rings with respect to the Rosenbloom-Tsfasman
metric. Special issue for ICMSAOŠ05 First International Conference On Modeling, Simulation
and Applied Optimization, The Franklin Institute Journal, 5:790-799, 2007.
[8] F.J. MacWilliams and N.J.A Sloane. The theory of error correcting codes. North-Holland
Pub. Co., 1977.
[9] B.R.McDonald, Finite rings with identity, Pure and AppliedMathematics.Marcel Dekker.
1974.
[10] E. Saltürk and˙I. ¸Siap. On the number of linear codes over Zpm, submitted.
[11] E. Saltürk and˙I. ¸Siap. The total number of linear codes over Fq +uFq, submitted.
[12] N.J.A. Sloane. On-line encyclopedia of integer sequences. Published electronically at
http://www.resear
h.att.
om/njas/sequen
es.
[13] Z.X. Wan. Quaternary codes. Series on Applied Mathematics, World Scientific Publisher
Co., Singapore, 1997.
[14] Y. Yeh. On prime power abelian groups. Bull. AMS, 54:323-327, 1948.

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