MAIN DIRECTIONS

Main directions in my research activity

1. Curves over finite fields with many rational points and automorphisms group of algebraic curves

• Automorphisms groups [2013/1]

• Maximal curves [2020/7] [2021/12] [2021/14]

2. Varieties over finite fields

• Bounds [2016/5]

• Hermitian variety [2018/7] 

3. Construction and classification of relevant objects in affine and projective spaces over finite fields 

• Caps [2011/1] [2012/2] [2013/4] [2014/2] [2014/8] [2015/3] [2017/3] [2017/5] [2017/6] [2017/7] [2017/10] [2018/5] [2019/6]

• Arcs in projective planes [2012/1] [2013/2] [2013/3] [2013/5] [2013/6] [2014/4] [2015/2] [2016/1] [2018/12] 

• k-arcs in projective planes [2014/1] [2016/6] [2017/4][2017/9] [2022/11]

• Arcs in projective spaces [2015/1] 

• Saturating sets [2013/5] [2013/7] [2013/7]

• Semiovals [2014/3] [2016/4] [2018/15]

• Semiarcs [2014/6]

• Ovoid in polar spaces [2022/13]

4. Linear codes and connections with geometric structures

• MDS codes [2015/1] 

• NMDS codes [2014/1]

• Functional codes [2014/5] [2014/7] [2019/1]

• Quantum codes [2012/2] [2014/8] [2021/11]

• Covering codes [2015/4] [2016/8] [2019/5] [2020/6]

• Additive codes [2015/5]

• Subspace codes [2016/2][2017/8][2021/5] 

• Reed-Muller codes [2016/5]

• AG codes [2018/3] [2018/9] [2018/11] [2018/14] [2021/2] [2021/11]

• Minimal codes and minimal codewords in codes [2019/2] [2019/3] [2021/8] [2021/13] [2022/10] [2023/1] [2023/2]

• Locally recoverable codes [2020/11]

• Rank-metric codes [2022/8] [2023/4] 

5. Permutation polynomials and permutation functions

• Permutation polynomials [2018/1] [2018/2] [2018/8] [2018/10] [2020/1] [2021/3][2021/6] [2021/17]

• Complete permutation polynomials [2016/7] [2017/2]

• Permutation rational functions [2021/10]

6. Small value sets functions

[2021/1] [2022/2]

7. PN/APN functions and their generalizations

• Planar functions in characteristic two [2019/4] [2020/2]

• Planar functions in odd characteristic [2022/3]

• P(c)N functions [2020/5] [2021/7] [2022/12]

• APN and GAPN functions [2022/4] [2022/6] [2022/7]

• Crooked functions[2022/9]

8. Scattered linear sets and their generalizations

• Maximum scattered linear sets [2018/5] [2020/3] [2023/5]

• Scattered polynomials and their generalizations [2021/4] [2018/6] [2020/10] [2021/15] [2022/1] [2022/5]

• Evasive subspaces [2021/16]

9. Semifields

[2017/1] [2018/4]

10. Graphs from geometric structures

[2018/13] [2020/4] [2020/9]