K.Feng is working on algebraic number theory and coding theory.

On number theory, he is interested in the galois structure of class group and unit group of global fields(both number and function fields). He is also interested in the arithmetic theory on elliptic curves, particularly, to determine the rank for several series of elliptic curves and to verify the Birch-Swinnerton-Dyer conjecture for them.

On coding theory, he is interested in constructing good algebraic-geometry codes and quantum error-correcting codes.

Main publications

[1] K.Feng and Fei Xu, Kolyvagin’s Euler systems in cyclotomic function fields, JNT 57(1996), 114-121.

[2] K.Feng and W.-C.W.Li, Spectra of hypergraphs and applications, JNT 60(1996), 1-22.

[3] K.Feng, Non-congruent numbers, odd graphes and the Birth-Swinnerton-Dyer conjecture, Acta Arith. 75(1996), 71-83.

[4] K.Feng, Anderson’s root numbers and Thakur’s gauss sums, JNT 65(1997), 179-296.

[5] K.Feng, Cyclotomic Function Fields, Shanghai, 1997.

[6] K.Feng, P.Shiue and Qing Xiang, On aperiodic and periodic complementary binary sequences, IEEE Trans. IT-45(1999), 296-303.

[7] K.Feng, Generalized bent functions and class number of imaginary quadratic fields, Science in china, ser, A, 24(2000), 1-8.

[8] K.Feng, Algebraic Number Theory, Science Pub. Com. Beijing, 2000.