On-orbit codes of posets and operators in algebra
For a partition μ of a positive integer and a prime p , let A ( p , μ ) be a finite Abelian p -group, and let A ^ ( p , μ ) be its dual group. We define a finite Abelian group as G = ⨁ A ( p , μ ) and its dual as G ^ = ⨁ A ^ ( p , μ ) . In this paper, we explore the symplectic structure associated w...
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| Vydáno v: | Journal of algebraic combinatorics Ročník 62; číslo 3; s. 44 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
Springer US
01.11.2025
Springer Nature B.V |
| Témata: | |
| ISSN: | 0925-9899, 1572-9192 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | For a partition
μ
of a positive integer and a prime
p
, let
A
(
p
,
μ
)
be a finite Abelian
p
-group, and let
A
^
(
p
,
μ
)
be its dual group. We define a finite Abelian group as
G
=
⨁
A
(
p
,
μ
)
and its dual as
G
^
=
⨁
A
^
(
p
,
μ
)
. In this paper, we explore the symplectic structure associated with the group
Z
(
p
,
μ
)
=
A
(
p
,
μ
)
⊕
A
^
(
p
,
μ
)
and consider its action on the Hilbert space
L
2
(
G
)
.
We investigate the correspondence between the ideals of a poset, which represent the sizes of bit strings, and the lengths of
automorphism orbit code words
. We also examine the orbits that result from the action of the symplectic structure on the group
Z
(
p
,
μ
)
. Additionally, we present a study of
μ
-based poset orbit codes and the operators of the algebra
H
o
m
C
(
L
2
(
G
)
,
L
2
(
G
)
)
. This interaction among the order ideals of a poset,
μ
-based poset orbit codes, group symmetries, and the operators in the algebra
H
o
m
C
(
L
2
(
G
)
,
L
2
(
G
)
)
bridges the gap between combinatorial coding theory and quantum systems. It also provides practical insights for constructing quantum protocols in the context of modern quantum information theory and cryptography. |
|---|---|
| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0925-9899 1572-9192 |
| DOI: | 10.1007/s10801-025-01469-5 |