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...
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| Published in: | Designs, codes, and cryptography Vol. 90; no. 7; pp. 1659 - 1677 |
|---|---|
| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
New York
Springer US
01.07.2022
Springer Nature B.V |
| Subjects: | |
| ISSN: | 0925-1022, 1573-7586 |
| Online Access: | Get full text |
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| Summary: | 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
}
. |
|---|---|
| Bibliography: | 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 |