Information sets as permutation cycles for quadratic residue codes
The two cases p=7 and p=23 are the only known cases where the automorphism group of the [p+1, (p+1)/2] extended binary quadratic residue code, O(p), properly contains PSL(2,p). These codes have some of their information sets represented as permutation cycles from Aut(Q(p)). Analysis proves that al...
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| Format: | Article |
| Language: | English |
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Wiley
1982-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171282000398 |
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| _version_ | 1832547403773771776 |
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| author | Richard A. Jenson |
| author_facet | Richard A. Jenson |
| author_sort | Richard A. Jenson |
| collection | DOAJ |
| description | The two cases p=7 and p=23 are the only known cases where the automorphism group of the [p+1, (p+1)/2] extended binary quadratic residue code, O(p), properly contains PSL(2,p). These codes have some of their information sets represented as permutation cycles from Aut(Q(p)). Analysis proves that all information sets of Q(7) are so represented but those of Q(23) are not. |
| format | Article |
| id | doaj-art-01e56bb7daaf4ee48dc0bcb46488abaa |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1982-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-01e56bb7daaf4ee48dc0bcb46488abaa2025-02-03T06:44:49ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251982-01-015240340610.1155/S0161171282000398Information sets as permutation cycles for quadratic residue codesRichard A. Jenson0Department of Mathematics, Boston College, Chestnut Hill, Massachusetts, USAThe two cases p=7 and p=23 are the only known cases where the automorphism group of the [p+1, (p+1)/2] extended binary quadratic residue code, O(p), properly contains PSL(2,p). These codes have some of their information sets represented as permutation cycles from Aut(Q(p)). Analysis proves that all information sets of Q(7) are so represented but those of Q(23) are not.http://dx.doi.org/10.1155/S0161171282000398binary codeautomorphism group of a codeinformation setMathieu group of degree 24orbit. |
| spellingShingle | Richard A. Jenson Information sets as permutation cycles for quadratic residue codes International Journal of Mathematics and Mathematical Sciences binary code automorphism group of a code information set Mathieu group of degree 24 orbit. |
| title | Information sets as permutation cycles for quadratic residue codes |
| title_full | Information sets as permutation cycles for quadratic residue codes |
| title_fullStr | Information sets as permutation cycles for quadratic residue codes |
| title_full_unstemmed | Information sets as permutation cycles for quadratic residue codes |
| title_short | Information sets as permutation cycles for quadratic residue codes |
| title_sort | information sets as permutation cycles for quadratic residue codes |
| topic | binary code automorphism group of a code information set Mathieu group of degree 24 orbit. |
| url | http://dx.doi.org/10.1155/S0161171282000398 |
| work_keys_str_mv | AT richardajenson informationsetsaspermutationcyclesforquadraticresiduecodes |