| 1. |
- Heden, Olof
(författare)
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Linear maps of perfect codes and irregular C-partitions
- 2015
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Ingår i: Discrete Mathematics. - : Elsevier BV. - 0012-365X .- 1872-681X. ; 338:3, s. 149-163
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Tidskriftsartikel (refereegranskat)abstract
- The concept of an irregular C-partition of binary space into perfect 1-error-correcting codes is defined. Three distinct constructions of irregular C-partitions are presented. The relation between irregular C-partitions and linear maps, that map perfect codes to perfect codes, is discussed
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| 2. |
- Heden, Olof, et al.
(författare)
-
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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| 3. |
- Heden, Olof, et al.
(författare)
-
On the existence of a (2,3)-spread in V(7,2)
- 2016
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Ingår i: Ars combinatoria. - : Charles Babbage Research Centre. - 0381-7032. ; 124, s. 161-164
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Tidskriftsartikel (refereegranskat)abstract
- An (s, t)-spread in a finite vector space V = V (n, q) is a collection F of t-dimensional subspaces of V with the property that every s-dimensional subspace of V is contained in exactly one member of F. It is remarkable that no (s, t)-spreads has been found yet, except in the case s = 1. In this note, the concept a-point to a (2,3)-spread F in V = V(7, 2) is introduced. A classical result of Thomas, applied to the vector space V, states that all points of V cannot be alpha-points to a given (2, 3)-spread.F. in V. In this note, we strengthened this result by proving that every 6-dimensional subspace of V must contain at least one point that is not an a-point to a given (2, 3)-spread of V.
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| 4. |
- Heden, Olof, et al.
(författare)
-
Perfect 1-error-correcting Lipschitz weight codes
- 2016
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Ingår i: Mathematical Communications. - : Udruga Matematicara Osijek. - 1331-0623 .- 1848-8013. ; 21:1, s. 23-30
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Tidskriftsartikel (refereegranskat)abstract
- Let pi be a Lipschitz prime and p = pi pi(star). Perfect 1-error-correcting codes in H(Z)(n)(pi), are constructed for every prime number p equivalent to 1(mod 4). This completes a result of the authors in an earlier work, Perfect Mannheim, Lipschitz and Hurwitz weight codes, (Math. Commun. 19(2014), 253-276), where a construction is given in the case p 3 (mod 4).
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