21. |
- Heden, Olof
(författare)
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Maximal partial spreads in PG(3,5)
- 2000
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Ingår i: Ars combinatoria. - 0381-7032. ; 57, s. 97-101
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Tidskriftsartikel (refereegranskat)abstract
- Maximal partial spreads of the sizes 13, 14, 15,..., 22 and 26 are described. They were found by using a computer. The computer also made a complete search for maximal partial spreads of size less then or equal to 12. No such maximal partial spreads were found.
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22. |
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23. |
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24. |
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25. |
- Heden, Olof
(författare)
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On kernels of perfect codes
- 2010
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Ingår i: Discrete Mathematics. - : Elsevier BV. - 0012-365X .- 1872-681X. ; 310:21, s. 3052-3055
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Tidskriftsartikel (refereegranskat)abstract
- It is shown that there exists a perfect one-error-correcting binary code with a kernel which is not contained in any Hamming code.
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26. |
- Heden, Olof, et al.
(författare)
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On linear equivalence and phelps codes
- 2010
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Ingår i: Advances in Mathematics of Communications. - : American Institute of Mathematical Sciences (AIMS). - 1930-5346 .- 1930-5338. ; 4:1, s. 69-81
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Tidskriftsartikel (refereegranskat)abstract
- It is shown that all non-full-rank FRH-codes, a class of perfect codes we define in this paper, are linearly equivalent to perfect codes obtainable by Phelps' construction. Moreover, it is shown by an example that the class of perfect FRH-codes also contains perfect codes that are not obtainable by Phelps construction.
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27. |
- Heden, Olof, et al.
(författare)
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On linear equivalence and Phelps codes
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- It is shown that all the non full rank FRH-codes, a class of perfect codes we define in the paper, are linearly equivalent to perfect codes obtainable by Phelps construction. It is shown by an example that this class of perfect codes also contains perfect codes that are not obtainable by Phelps construction.
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28. |
- Heden, Olof, et al.
(författare)
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On linear equivalence and phelps codes. Addendum
- 2011
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Ingår i: Advances in Mathematics of Communications. - : American Institute of Mathematical Sciences (AIMS). - 1930-5346. ; 5:3, s. 543-546
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Tidskriftsartikel (refereegranskat)abstract
- A new class of perfect 1-error correcting binary codes, so called RRH-codes, are identified, and it is shown that every such code is linearly equivalent to a perfect code obtainable by the Phelps construction.
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29. |
- Heden, Olof, et al.
(författare)
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On perfect 1-epsilon-error-correcting codes
- 2015
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Ingår i: Mathematical Communications. - : Udruga Matematicara Osijek. - 1331-0623 .- 1848-8013. ; 20:1, s. 23-35
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Tidskriftsartikel (refereegranskat)abstract
- We generalize the concept of perfect Lee-error-correcting codes, and present constructions of this new class of perfect codes that are called perfect 1-epsilon-error-correcting codes. We also show that in some cases such codes contain quite a few perfect 1-error-correcting q-ary Hamming codes as subsets.
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30. |
- Heden, Olof
(författare)
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On perfect codes over non prime power alphabets
- 2010
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Ingår i: ERROR-CORRECTING CODES, FINITE GEOMETRIES AND CRYPTOGRAPHY. ; , s. 173-184
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Konferensbidrag (refereegranskat)abstract
- Known results on perfect codes over alphabets with q elements where q is not a prime power is surveyed. Some tools recently developed for the study of perfect 1-error correcting binary codes are generalized to the case of non prime power alphabets. A theorem by H. W. Lenstra from 1972 on the algebraic structure of perfect codes over non prime power alphabets will, by using this generalization, be further strengthened.
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