Title data
Kiermaier, Michael:
Codes from translation schemes on Galois rings of characteristic 4.
In: Electronic Notes in Discrete Mathematics.
Vol. 40
(15 May 2013)
.
 pp. 175180.
ISSN 15710653
DOI: https://doi.org/10.1016/j.endm.2013.05.032
Project information
Project title: 



Project financing: 
Deutsche Forschungsgemeinschaft 
Abstract in another language
In [4], it has been shown that the Teichmüller point set in the projective Hjelmslev geometry PHG(Rᵏ) over a Galois ring R of characteristic 4 with k odd is a twointersection set. From this result, the parameters of the generated codes can be derived, see [8, Fact 5.2]. The resulting Teichmüller Codes have a high minimum distance.
The key step in the proof of the twoweight property in [4] is to show that for a certain supergroup In [4], it has been shown that the Teichmüller point set in the projective Hjelmslev geometry PHG(Rᵏ) over a Galois ring R of characteristic 4 with k odd is a twointersection set. From this result, the parameters of the generated codes can be derived, see [8, Fact5.2]. The resulting Teichmüller Codes have a high minimum distance. of the Teichmüller units T in a Galois ring S of characteristic 4, the partition A_Σ = {{0},2S^*, Σ, S^*\Σ} induces a translation scheme on (S,+). We generalize these results by characterizing all supergroups Σ of T such that A_Σ induces a symmetric translation scheme. In turn, we get new twointersection sets in projective Hjelmslev geometries and two new series T_q,k,s and U_q,k,s of Rlinear codes. The series T_q,k,s generalizes the Teichmüller codes (special case s=0). The codes U_q,k,s are homogeneous twoweight codes. Application of the dualization construction to T_q,k,s yields another series T^*_q,k,s. The Gray images of the codes T_q,k,s and T^*_q,k,s have a higher minimum distance than all known F_qlinear codes of the same length and size.
Further data
Item Type:  Article in a journal 

Refereed:  Yes 
Additional notes:  This article belongs to a special issue: Combinatorics 2012 ed. by
Giorgio Faina 
Keywords:  ringlinear code; Teichmüller group; association scheme; homogeneous weight; projective Hjelmslev geometry 
Institutions of the University:  Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics 
Result of work at the UBT:  Yes 
DDC Subjects:  500 Science > 510 Mathematics 
Date Deposited:  20 Nov 2014 07:58 
Last Modified:  22 Jan 2015 07:00 
URI:  https://eref.unibayreuth.de/id/eprint/3725 