Cyclic codes over ℤ4 locator polynomials, and newton's identities

IEEE Transactions on Information Theory

Volumn 42, Issue 1, 1996, Pages 217-226

  Calderbank, A R ^a,b   McGuire, Gary ^a,c,d   Kumar, P Vijay ^a,e   Helleseth, Tor ^a,f  

^a IEEE

^b LUCENT TECHNOLOGIES   (United States)

^c CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^d University of Virginia   (United States)

^e UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

^f UNIVERSITY OF BERGEN   (Norway)

Author keywords

Codes over rings; Cyclic codes; Galois rings; Locator polynomials; Newton's identities

Indexed keywords

BINARY CODES; COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; ERROR CORRECTION; FOURIER TRANSFORMS; FUNCTIONS; POLYNOMIALS;

ALGEBRAIC GEOMETRY; CODES OVER RINGS; CYCLIC CODES; GALOIS RINGS; GRAY IMAGE; LINEAR CODES; LOCATOR POLYNOMIALS; NEWTON IDENTITIES;

INFORMATION THEORY;

EID: 0029774707     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.481791     Document Type: Article

References (13)

1. A. Bonnecaze, A. R. Calderbank, and P. Sole, "Quaternary quadratic residue codes and unimodular lattices," IEEE Trans. Inform. Theory, vol. 41, pp. 366-377, 1995.
2. 37, 12) Code via Galois Rings, preprint, 1994.
3. A. R. Calderbank and D. B. Wales, "Multiplying vectors in binary quadratic residue codes," SIAM J. Alg. Disc. Methods, vol. 3, no. 1, pp. 43-55, 1982.
4. J. H. Conway and N. J. A. Sloane, Sphere Packings Lattices and Groups. New York: Springer-Verlag, 1988.
5. M. D. Fried and M. Jarden, Field Arithmetic. New York: Springer-Verlag, 1986.
6. W. Fulton, Algebraic Curves. New York: Benjamin, 1969.
7. 4 -linearity of Kerdock, Preparata, Goethals, and related codes," IEEE Trans. Inform. Theory, vol. 40, pp. 301-319, 1994.
8. A. M. Kerdock, "A class of low-rate nonlinear binary codes," Inform. Contr., vol. 20, pp. 182-187. 1972.
9. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes. Amsterdam, The Netherlands: North-Holland, 1977.
10. O. Moreno and C. Moreno, "Exponential sums and Goppa Codes II," IEEE Trans. Inform. Theory, vol. 38, pp. 1222-1229, 1992.
11. 4, preprint 1995.
12. F. P. Preparata, "A class of optimum nonlinear double-error correcting codes," Inform. Contr., vol. 13, pp. 378-400, 1968.
13. T. Verhoeff, "An updated table of minimum-distance bounds for binary linear codes," IEEE Trans. Inform. Theory, vol. 39, pp. 662-667, 1993.