1. Baumert, L.D., McEliece, R.J.: Weights of irreducible cyclic codes. Information and Control 20, 158–175 (1972)

   Article MathSciNet MATH  Google Scholar 

2. Baumert, L.D., Mykkeltveit, J.: Weight distributions of some irreducible cyclic codes. DSN Progress Report 16, 128–131 (1973)

   Google Scholar 

3. Calderbank, A.R., Goethals, J.-M.: Three-weight codes and association schemes. Philips J. Res. 39, 143–152 (1984)

   MathSciNet MATH  Google Scholar 

4. Calkin, N.J., Key, J.D., de Resmini, M.J.: Minimum weight and dimension formulas for some geometric codes. Designs, Codes and Cryptography 17, 105–120 (1999)

   Article MathSciNet MATH  Google Scholar 

5. Delsarte, P., Goethals, J.M.: Irreducible binary cyclic codes of even dimension. In: Proc. Second Chapel Hill Conf. on Combinatorial Mathematics and Its Applications, Univ. North Carolina, Chapel Hill, NC, pp. 100–113 (1970)

   Google Scholar 

6. Ding, C.: The weight distribution of some irreducible cyclic codes. IEEE Trans. Inform. Theory (to appear)

   Google Scholar 

7. Ding, C., Luo, J., Niederreiter, H.: Two-weight codes punctured from irreducible cyclic codes. In: Li, Y., Ling, S., Niederreiter, H., Wang, H., Xing, C., Zhang, S. (eds.) Proc. of the First International Workshop on Coding Theory and Cryptography, pp. 119–124. World Scientific, Singapore (2008)

   Google Scholar 

8. Ding, C., Niederreiter, H.: Cyclotomic linear codes of order 3. IEEE Trans. Inform. Theory 53, 2274–2277 (2007)

   Article MathSciNet MATH  Google Scholar 

9. Goethals, J.M.: Factorization of cyclic codes. IEEE Trans. Inform. Theory 13, 242–246 (1967)

   Article MathSciNet  Google Scholar 

10. Griera, M.: On s-sums-sets (s odd) and three-weight projective codes. In: Proc. AAECC, pp. 68–76 (1986)

    Google Scholar 

11. Helleseth, T., Kløve, T., Mykkeltveit, J.: The weight distribution of irreducible cyclic codes with block length\(n_1((q^l-1)/N)\). Discrete Math. 18, 179–211 (1977)

    Article MathSciNet MATH  Google Scholar 

12. Langevin, P.: A new class of two weight codes. In: Cohen, S., Niederreiter, H. (eds.) Finite Fields and Applications, pp. 181–187. Cambridge University Press, Cambridge (1996)

    Chapter  Google Scholar 

13. MacWilliams, F., Seery, J.: The weight distributions of some minimal cyclic codes. IEEE Trans. Inform. Theory 27, 796–806 (1981)

    Article MathSciNet MATH  Google Scholar 

14. Myerson, G.: Period polynomials and Gauss sums for finite fields. Acta Arith. 39, 251–264 (1981)

    MathSciNet MATH  Google Scholar 

15. McEliece, R.J.: A class of two-weight codes. Jet Propulsion Laboratory Space Program Summary 37–41 IV, 264–266

    Google Scholar 

16. McEliece, R.J.: Irreducible cyclic codes and Gauss sums. In: Combinatorics, Part 1: Theory of Designs, Finite Geometry and Coding Theory. Math. Centre Tracts, vol. 55, pp. 179–196. Math. Centrum, Amsterdam (1974)

    Google Scholar 

17. McEliece, R.J., Rumsey Jr., H.: Euler products, cyclotomy, and coding. J. Number Theory 4, 302–311 (1972)

    Article MathSciNet MATH  Google Scholar 

18. Moisio, M.J., Väänen, K.O.: Two recursive algorithms for computing the weight distribution of certain irreducible cyclic codes. IEEE Trans. Inform. Theory 45, 1244–1249 (1999)

    Article MathSciNet MATH  Google Scholar 

19. Ray-Chaudhuri, D.K., Xiang, Q.: New necessary conditions for abelian Hadamard difference sets. J. of Statistical Planning and Inference 62, 69–79 (1997)

    Article MathSciNet MATH  Google Scholar 

20. Schmidt, B., White, C.: All two-weight irreducible cyclic codes? Finite Fields Appl. 8, 1–17 (2002)

    Article MathSciNet MATH  Google Scholar 

21. Segal, R., Ward, R.L.: Weight distributions of some irreducible cyclic codes. Mathematics of Computation 46, 341–354 (1986)

    Article MathSciNet MATH  Google Scholar 

22. Storer, T.: Cyclotomy and Difference Sets. Markham, Chicago (1967)

    MATH  Google Scholar 

23. Van der Vlugt, M.: On the weight hierarchy of irreducible cyclic codes. J. Comb. Theory Ser. A 71, 159–167 (1995)

    Article MathSciNet MATH  Google Scholar 

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