Using permutation rational functions to obtain permutation arrays with large hamming distance
We consider permutation rational functions ( PRFs ), V ( x )/ U ( x ), where both V ( x ) and U ( x ) are polynomials over a finite field F q . Permutation rational functions have been the subject of several recent papers. Let M ( n , D ) denote the maximum number of permutations on n symbols with...
Uložené v:
| Vydané v: | Designs, codes, and cryptography Ročník 90; číslo 7; s. 1659 - 1677 |
|---|---|
| Hlavní autori: | , , , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
New York
Springer US
01.07.2022
Springer Nature B.V |
| Predmet: | |
| ISSN: | 0925-1022, 1573-7586 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Shrnutí: | We consider permutation rational functions (
PRFs
),
V
(
x
)/
U
(
x
), where both
V
(
x
) and
U
(
x
) are polynomials over a finite field
F
q
. Permutation rational functions have been the subject of several recent papers. Let
M
(
n
,
D
) denote the maximum number of permutations on
n
symbols with pairwise Hamming distance
D
. Computing lower bounds for
M
(
n
,
D
) is the subject of current research with applications in error correcting codes. Using
PRFs
of specified degrees
d
we obtain improved lower bounds for
M
(
q
,
q
-
k
)
for prime powers
q
and
k
∈
{
5
,
6
,
7
,
8
,
9
}
, and for
M
(
q
+
1
,
q
-
k
)
for prime powers
q
and
k
∈
{
4
,
5
,
6
,
7
,
8
,
9
}
. |
|---|---|
| Bibliografia: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0925-1022 1573-7586 |
| DOI: | 10.1007/s10623-022-01039-x |