Mixed Materials
Galois hulls of constacyclic codes over affine algebra rings
| Τίτλος: | Galois hulls of constacyclic codes over affine algebra rings |
|---|---|
| Additional Titles: | Let $\mathcal A$ the affine algebra given by the ring $\mathbb{F}_q[X_1,X_2,\ldots,X_\ell]/ I$, where $I$ is the ideal $\langle t_1(X_1), t_2(X_2), \ldots, t_\ell(X_\ell) \rangle$ with each $t_i(X_i)$, $1\leq i\leq \ell$, being a square-free polynomial over $\mathbb{F}_q$. This paper studies the $k$-Galois hulls of $λ$-constacyclic codes over $\mathcal A$ regarding their idempotent generators. For this, first, we define the $k$-Galois inner product over $\mathcal A$ and find the form of the generators of the $k$-Galois dual and the $k$-Galois hull of a $λ$-constacyclic code over $\mathcal A$. Then, we derive a formula for the $k$-Galois hull dimension of a $λ$-constacyclic code. Further, we provide a condition for a $λ$-constacyclic code to be $k$-Galois LCD. Finally, we give some examples of the use of these codes in constructing entanglement-assisted quantum error-correcting codes. |
| Συγγραφείς: | Debnath, Indibar, Islam, Habibul, Martínez-Moro, Edgar, Prakash, Om |
| Στοιχεία εκδότη: | 2024-12-11 |
| Τύπος εγγράφου: | Mixed materials |
| Όροι ευρετηρίου: | Information Theory, 94B05, 94B15, 94B60, text |
| Σύνδεσμος: | |
| Διαθεσιμότητα: | Open access content. Open access content |
| Other Numbers: | COO oai:arXiv.org:2412.08512 1504904852 |
| Πηγή συνεισφοράς: | CORNELL UNIV From OAIster®, provided by the OCLC Cooperative. |
| Αριθμός Καταχώρησης: | edsoai.on1504904852 |
| Βάση Δεδομένων: | OAIster |
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