Aimo Tietäväinen - Publications

June 1999

Articles in international refereed journals and books

Articles in refereed conference proceedings

Articles in Finnish journals with referee practice

Other scientific publications


Articles in international refereed journals and books

1. On the non-trivial solvability of some systems of equations in finite fields. - Ann. Univ. Turku. A I 71 (1964) 1-5.
2. On the non-trivial solvability of some equations and systems of equations in finite fields. - Ann. Acad. Sci. Fenn. A I 360 (1965) 1-38.
3. On systems of linear and quadratic equations in finite fields. - Ann. Acad. Sci. Fenn. A I 382 (1965) 1-5.
4. On systems of equations in finite fields. Ann. Acad. Sci. Fenn. A I 386 (1966) 1-10.
5. On the trace of a polynomial over a finite field. - Ann. Univ. Turku. A I 87 (1966) 1-7.
6. On non-residues of a polynomial. - Ann. Univ. Turku. A I 94 (1966) 1-6.
7. On the solvability of equations in incomplete finite fields. - Ann. Univ. Turku. A I 102 (1967) 1-13.
8. On pairs of additive equations. - Ann. Univ. Turku. A I 112 (1967) 1-7.
9. On diagonal forms over finite fields. - Ann. Univ. Turku A I 118 (1968) 1-10.
10. On the distribution of the residues of a polynomial. - Ann. Univ. Turku. A I 120 (1968) 1-4.
11. On a homogeneous congruence of odd degree. - Ann. Univ. Turku. A I 131 (1969) 1-6.
12. On the nonexistence of perfect 4-Hamming-error-correcting codes. - Ann. Acad. Sci. Fenn. A I 485 (1970) 1-6.
13. On a problem of Chowla and Shimura. - J. Number Theory 3 (1971) 247-252.
14. (with A. Perko) There are no unknown perfect binary codes. - Ann. Univ. Turku. A I 148 (1971) 1-10.
15. Note on Waring's problem (mod p). - Ann. Acad. Sci. Fenn. A I 554 (1973) 1-7.
16. On the nonexistence of perfect codes over finite fields. - SIAM J. Appl. Math. 24 (1973) 88-96.
17. A short proof for the nonexistence of unknown perfect codes over GF(q), q > 2. - Ann. Acad. Sci. Fenn. A I 580 (1974) 1-5.
18. Proof of a conjecture of S. Chowla. - J. Number Theory 7 (1975) 353-356.
19. (with M. Dodson) A note on Waring's problem in GF(p). - Acta Arithmetica 30 (1976) 159-167.
21. Nonexistence of nontrivial perfect codes in case $q=p^r_1p^s_2$, $e\geq 3$. - Discrete Mathematics 17 (1977) 199-205.
23. Bounds for binary codes just outside the Plotkin range. - Information and Control 47 (1980) 85-93.
24. Character sums and coding theory. - Ars Combinatoria 16-B (1983) 197-200.
25. Lower bounds for the maximum moduli of certain character sums. - J. London Math. Soc. (2) 29 (1984) 204-210.
27. Character sum applications of coding theory. - Ann. Univ. Turku. A I 186 (1984) 110-117.
29. On the covering radius of long binary BCH codes. - Discrete Applied Mathematics 16 (1987) 75-77.
31. Incomplete sums and two applications of Deligne's result. - Springer-Verlag: Lecture Notes in Mathematics 1352: Algebra. Some Current Trends (1988) 190-205.
32. Codes and character sums. - Springer-Verlag: Lecture Notes in Computer Science 388: Coding Theory and Applications (1989) 3-12.
34. An asymptotic bound on the covering radii of binary BCH codes. - IEEE Transactions on Information Theory 36 (1990) 211-213.
36. An upper bound on the covering radius as a function of the dual distance. - IEEE Transactions on Information Theory 36 (1990) 1472-1474.
37. Covering radius and dual distance. - Designs, Codes and Cryptography 1 (1991) 31-46.
38. On the correlation of sequences. - Springer-Verlag: Lecture Notes in Computer Science 573: Algebraic Coding (1992) 1-4.
39. On the cardinality of sets of sequences with given maximum correlation. - Discrete Mathematics 106/107 (1992) 471-477.
40. (with S. Litsyn) Character sum constructions of constrained error-correcting codes. - Applicable Algebra in Engineering, Communication and Computing 5 (1994) 45-51.
41. (with H. Tarnanen) A simple method to estimate the maximum nontrivial correlation of some sets of sequences. - Applicable Algebra in Engineering, Communication and Computing 5 (1994) 123-128.
44. (with I. Honkala and S. Litsyn) On algebraic methods in covering radius problems. - Lecture Notes in Computer Science 948: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (1995) 21-32.
45. (with S. Litsyn) Upper bounds on the covering radius of a code with a given dual distance. - European Journal of Combinatorics 17 (1996) 265-270.
46. (with I. Honkala and Y. Kaipainen) Long binary BCH codes are normal. - Applicable Algebra in Engineering, Communication and Computing 8 (1997) 49-55.
49. (with P. Charpin and V. Zinoviev) On binary cyclic codes with d = 3. - Problems of Information Transmission 33 (1997), 287-296.
52. (= 48) Vinogradov's method and some applications. In: Number Theory and Its Applications, edited by C. Yildirim and S.A. Stepanov. Marcel Dekker 1998, pp. 261-282.
53. (with I. Honkala) Codes and number theory. In: Handbook of Coding Theory, edited by V.S. Pless and W.C. Huffman. Elsevier 1998, pp. 1141-1194.
54. (with P. Charpin and V. Zinoviev) On the minimum distances of non-binary cyclic codes. - Designs, Codes and Cryptography (accepted).
55. A method to estimate partial-period correlations. In: Numbers, Information and Complexity, edited by B. Balkenhol and U. Tamm. Kluwer (submitted).
Remark: The method which Ann. Acad. Sci. Fenn. and Ann. Univ. Turku used in the sixties was probably a modification of the referee practice.,

Articles in refereed conference proceedings

20. Some recent results on perfect codes. - Colloquia Mathematica Societatis Janos Bolyai 20. Algebraic Theory of Semigroups, Szeged (Hungary) (1976) 647-655.
22. Non-binary Johnson schemes. - The Fifth International Symposium on Information Theory. Abstracts of Papers II (1979) 112.
28. Character sums and block codes. - The Sixth International Symposium on Information Theory. Abstracts of Papers II (1984) 254-256.
30. The covering radius problem and character sums. - Algebraic and Combinatorial Coding Theory. International Workshop in Varna. Proceedings (1988) 155-159.
33. Covering radius problems and character sums. - Proceedings of the Fourth Joint Swedish-Soviet International Workshop on Information Theory (1989) 196-198.
35. On the covering radii of Reed-Muller codes. - II International / Workshop "Algebraic and Combinatorial Coding Theory". Abstracts of / Papers (1990) 211-214.
42. (with I. Honkala and Y. Kaipainen) Long binary narrow-sense BCH codes are normal. - Proceedings of the 1994 IEEE International Symposium on Information Theory, Trondheim (1994) 48.
43. (with S. Litsyn and P. Sol‚) New upper bounds on the covering radius of codes with known dual distance. - Proceedings of the 1994 IEEE International Symposium on Information Theory, Trondheim (1994) 304.
47. (with P. Charpin and V. Zinoviev) On binary cyclic codes with minimum distance three. - Proceedings of the Fifth International Workshop on Algebraic and Combinatorial Coding Theory (ACCT 96) (1996) 93-97.
51. (with P. Charpin and V. Zinoviev) On the minimum distance of certain cyclic codes. - Proceedings of the IEEE International Symposium on Information Theory (1997) 505.

Articles in Finnish journals with referee practice

26. Virheitä korjaavista koodeista. - Arkhimedes 36 (1984) 11-18.

Other scientific publications

48. Vinogradov's method and some applications. - TUCS Technical Reports 28 (1996) 1-17.
50. (with P. Charpin and V. Zinoviev) On the divisibility of polynomials over finite fields. - TUCS Technical Reports 82 (1996), 1-4.