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Completing codes. (English) Zbl 0669.94012
Summary: The problem to characterize those finite codes that can be embedded in a finite maximal code is investigated. The main results, which give some necessary conditions for the embedding, are obtained by using factorizations of cyclic groups.

MSC:
94B05 Linear codes (general theory)
94B15 Cyclic codes
20K01 Finite abelian groups
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References:
[1] 1. J. BERSTEL and D. PERRIN, The Theory of Codes, Academic Press, 1985. Zbl0587.68066 MR797069 · Zbl 0587.68066
[2] 2. C. DE FELICE, Construction of a Family of Finite Maximal Codes, Report of L.I.T.P., 1987. · Zbl 0664.94022
[3] 3. C. DE FELICE and A. RESTIVO, Some Results on Finite Maximal Codes, R.A.I.R.O. Informatique Théorique, Vol. 19, No. 4, 1985. Zbl0578.68062 MR827484 · Zbl 0578.68062
[4] 4. A. EHRENFEUCHT and G. ROZEMBERG, Each Regular Code is Included in a Maximal Regular Code, R.A.I.R.O. Informat. Theor. Application, Vol. 20, 1986, pp. 89-96. Zbl0609.68053 MR849968 · Zbl 0609.68053
[5] 5. FUCHS, Abelian Group, Pergamon Press, 1960.
[6] 6. Al. A. MARKOV, An Example of an Indipendent System of Words which Cannot be Included in a Finite Complete System (Russian), Mat. Zametki, Vol. 1 1967, pp. 87-90. Zbl0154.00703 MR210594 · Zbl 0154.00703
[7] 7. M. KRASNER and B. RANULAC, Sur une propriété des polynomes de la division du cercle, C.R. Acad. Sci. Paris, T. 204, 1937, pp. 397-399. JFM63.0044.03 · Zbl 0015.38601
[8] 8. D. PERRIN and M. P. SCHUTZENBERGER, Un problème élémentaire de la théorie de l’information, Coll. Internat, du C.N.R.S., n^\circ 276, Théorie de l’Information, 1977. Zbl0483.94028 · Zbl 0483.94028
[9] 9. A. RESTIVO, On Codes Having no Finite Completion, Discrete Math., Vol. 17, 1977, pp. 309-316. Zbl0357.94011 MR498922 · Zbl 0357.94011
[10] 10. P. SHORA Counterexample to the Triangle Conjecture, J. Comb. Theory A, Vol. 38, 1985, pp. 110-112. Zbl0558.20032 MR773566 · Zbl 0558.20032
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