Matrix powers over finite fields
Let GF(q) denote the finite field of order q=pe with p odd. Let M denote the ring of 2×2 matrices with entries in GF(q). Let n denote a divisor of q−1 and assume 2≤n and 4 does not divide n. In this paper, we consider the problem of determining the number of n-th roots in M of a matrix B∈M. Also, as...
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| Format: | Article |
| Language: | English |
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Wiley
1992-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171292000991 |
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| _version_ | 1832547535029272576 |
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| author | Maria T. Acosta-De-Orozco Javier Gomez-Calderon |
| author_facet | Maria T. Acosta-De-Orozco Javier Gomez-Calderon |
| author_sort | Maria T. Acosta-De-Orozco |
| collection | DOAJ |
| description | Let GF(q) denote the finite field of order q=pe with p odd. Let M denote the ring of 2×2 matrices with entries in GF(q). Let n denote a divisor of q−1 and assume 2≤n and 4 does not divide n. In this paper, we consider the problem of determining the number of n-th roots in M of a matrix B∈M. Also, as a related problem, we consider the problem of lifting the solutions of X2=B over Galois rings. |
| format | Article |
| id | doaj-art-d3e21b8d1f5f4b9a94ab6948354f9f28 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1992-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d3e21b8d1f5f4b9a94ab6948354f9f282025-02-03T06:44:28ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251992-01-0115476777110.1155/S0161171292000991Matrix powers over finite fieldsMaria T. Acosta-De-Orozco0Javier Gomez-Calderon1Department of Mathematics, Penn State University, Beaver Campus, Monaca 15061, Pennsylvania, USADepartment of Mathematics, Penn State University, New Kensington Campus, New Kensington 15068, Pennsylvania, USALet GF(q) denote the finite field of order q=pe with p odd. Let M denote the ring of 2×2 matrices with entries in GF(q). Let n denote a divisor of q−1 and assume 2≤n and 4 does not divide n. In this paper, we consider the problem of determining the number of n-th roots in M of a matrix B∈M. Also, as a related problem, we consider the problem of lifting the solutions of X2=B over Galois rings.http://dx.doi.org/10.1155/S0161171292000991finite fields and matrix powers. |
| spellingShingle | Maria T. Acosta-De-Orozco Javier Gomez-Calderon Matrix powers over finite fields International Journal of Mathematics and Mathematical Sciences finite fields and matrix powers. |
| title | Matrix powers over finite fields |
| title_full | Matrix powers over finite fields |
| title_fullStr | Matrix powers over finite fields |
| title_full_unstemmed | Matrix powers over finite fields |
| title_short | Matrix powers over finite fields |
| title_sort | matrix powers over finite fields |
| topic | finite fields and matrix powers. |
| url | http://dx.doi.org/10.1155/S0161171292000991 |
| work_keys_str_mv | AT mariatacostadeorozco matrixpowersoverfinitefields AT javiergomezcalderon matrixpowersoverfinitefields |