| 1. |
- Guzeltepe, Murat, et al.
(författare)
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Perfect Mannheim, Lipschitz and Hurwitz weight codes
- 2014
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Ingår i: Mathematical Communications. - 1331-0623 .- 1848-8013. ; 19:2, s. 253-276
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Tidskriftsartikel (refereegranskat)abstract
- The set of residue classes modulo an element pi in the rings of Gaussian integers, Lipschitz integers and Hurwitz integers, respectively, is used as alphabets to form the words of error correcting codes. An error occurs as the addition of an element in a set E to the letter in one of the positions of a word. If epsilon is a group of units in the original rings, then we obtain the Mannheim, Lipschitz and Hurwitz metrics, respectively. Some new perfect 1-error-correcting codes in these metrics are constructed. The existence of perfect 2-error-correcting codes is investigated by computer search.
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| 2. |
- 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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| 3. |
- 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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