Quality characteristics of finite linear codes
DOI:
https://doi.org/10.34767/SIMIS.2014.17.01Keywords:
Linear codes, coding, Hamming distanceAbstract
Paper describes the qualitative properties of linear codes in the dimension of "half-width", ie. when the code dimension is equal to its co-dimension. The codes are constructed with use of Frobenius automorphism in a vector space over a finite field of the characteristic more than two. We considered three dimensions codes embedded in six dimensional space over the field with seven elements.
An analysis of the Hamming distance for such a codes is also represented in the paper.
References
Biswas S., Introduction to Codding Theory: Basic codes and Shannon’s theorem. http://www.math.uchicago.edu/
Frydrych M., Horzelski W., Generator kodów liniowych o skończonych charakterystykach, arXiv 11/2014, CoRRabs/1411, 2014.
MacWilliams F.J., Sloane N.J.A. , The Theory of ErrorCorrecting Codes. North-Holland Publishing Company,1978.
Pless V., Introduction to the Theory of Error-Correcting Codes. John Wiley and Sons, Inc., 1998.
Xiao-Yu Hu ,Fossorier, M.P.C., Eleftheriou, E., On the computation of the minimum distance of low-density paritycheck codess. Communications, IEEE International Conference, 2004.
