A recent survey of permutation trinomials over finite fields
Constructing permutation polynomials is a hot topic in the area of finite fields, and permutation polynomials have many applications in different areas. Recently, several classes of permutation trinomials were constructed. In 2015, Hou surveyed the achievements of permutation polynomials and novel m...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2023-10-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231495?viewType=HTML |
| _version_ | 1797628966971899904 |
|---|---|
| author | Varsha Jarali Prasanna Poojary G. R. Vadiraja Bhatta |
| author_facet | Varsha Jarali Prasanna Poojary G. R. Vadiraja Bhatta |
| author_sort | Varsha Jarali |
| collection | DOAJ |
| description | Constructing permutation polynomials is a hot topic in the area of finite fields, and permutation polynomials have many applications in different areas. Recently, several classes of permutation trinomials were constructed. In 2015, Hou surveyed the achievements of permutation polynomials and novel methods. But, very few were known at that time. Recently, many permutation binomials and trinomials have been constructed. Here we survey the significant contribution made to the construction of permutation trinomials over finite fields in recent years. Emphasis is placed on significant results and novel methods. The covered material is split into three aspects: the existence of permutation trinomials of the respective forms $ x^{r}h(x^{s}) $, $ \lambda_{1}x^{a}+\lambda_{2}x^{b}+\lambda_{3}x^{c} $ and $ x+x^{s(q^{m}-1)+1} +x^{t(q^{m}-1)+1} $, with Niho-type exponents $ s, t $. |
| first_indexed | 2024-03-11T10:46:40Z |
| format | Article |
| id | doaj.art-199f1ba6b6c64d209cc9ccd3afb14165 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-11T10:46:40Z |
| publishDate | 2023-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-199f1ba6b6c64d209cc9ccd3afb141652023-11-14T01:16:39ZengAIMS PressAIMS Mathematics2473-69882023-10-01812291822922010.3934/math.20231495A recent survey of permutation trinomials over finite fieldsVarsha Jarali 0Prasanna Poojary1G. R. Vadiraja Bhatta21. Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, India; varshapjarali@gmail.com2. Department of Mathematics, Manipal Institute of Technology Bengaluru, Manipal Academy of Higher Education, Manipal, India; poojary.prasanna@manipal.edu; poojaryprasanna34@gmail.com1. Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, India; varshapjarali@gmail.comConstructing permutation polynomials is a hot topic in the area of finite fields, and permutation polynomials have many applications in different areas. Recently, several classes of permutation trinomials were constructed. In 2015, Hou surveyed the achievements of permutation polynomials and novel methods. But, very few were known at that time. Recently, many permutation binomials and trinomials have been constructed. Here we survey the significant contribution made to the construction of permutation trinomials over finite fields in recent years. Emphasis is placed on significant results and novel methods. The covered material is split into three aspects: the existence of permutation trinomials of the respective forms $ x^{r}h(x^{s}) $, $ \lambda_{1}x^{a}+\lambda_{2}x^{b}+\lambda_{3}x^{c} $ and $ x+x^{s(q^{m}-1)+1} +x^{t(q^{m}-1)+1} $, with Niho-type exponents $ s, t $.https://www.aimspress.com/article/doi/10.3934/math.20231495?viewType=HTMLpermutation polynomialtrinomial permutationsniho-type exponentsbinomial permutations |
| spellingShingle | Varsha Jarali Prasanna Poojary G. R. Vadiraja Bhatta A recent survey of permutation trinomials over finite fields AIMS Mathematics permutation polynomial trinomial permutations niho-type exponents binomial permutations |
| title | A recent survey of permutation trinomials over finite fields |
| title_full | A recent survey of permutation trinomials over finite fields |
| title_fullStr | A recent survey of permutation trinomials over finite fields |
| title_full_unstemmed | A recent survey of permutation trinomials over finite fields |
| title_short | A recent survey of permutation trinomials over finite fields |
| title_sort | recent survey of permutation trinomials over finite fields |
| topic | permutation polynomial trinomial permutations niho-type exponents binomial permutations |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231495?viewType=HTML |
| work_keys_str_mv | AT varshajarali arecentsurveyofpermutationtrinomialsoverfinitefields AT prasannapoojary arecentsurveyofpermutationtrinomialsoverfinitefields AT grvadirajabhatta arecentsurveyofpermutationtrinomialsoverfinitefields AT varshajarali recentsurveyofpermutationtrinomialsoverfinitefields AT prasannapoojary recentsurveyofpermutationtrinomialsoverfinitefields AT grvadirajabhatta recentsurveyofpermutationtrinomialsoverfinitefields |