Projective MDS Codes Over GF(27)‎

Main Article Content

Emad Bakr Abdulkareem Al-Zangana


MDS code is a linear code that achieves equality in the Singleton bound, and projective MDS (PG-MDS) is MDS code with independents property of any two columns of its generator matrix.   In this paper, elementary methods for modifying a PG-MDS code of dimensions 2, 3, as extending and lengthening, in order to find new incomplete PG-MDS codes have been used over . Also, two complete PG-MDS codes over  of length  and 28 have been found.


Download data is not yet available.

Article Details

How to Cite
Abdulkareem Al-Zangana EB. Projective MDS Codes Over GF(27)‎. Baghdad Sci.J [Internet]. [cited 2021Jun.16];18(2(Suppl.):1125. Available from:


‎1.‎ MacWilliams FJ, Sloane NA. The Theory of error-correcting ‎codes. 6th ed. Amsterdam: North-Holland Publishing Company; ‎‎1977. 762 p.‎

‎2.‎ Cardell SD, Climent JJ, Requena V. A construction of MDS array ‎codes. WIT Transactions on Information and Communication ‎Technologies. 2013; 45(12): p. 47-58.‎

‎3.‎ Grassl M. Bounds on the minimum distance of linear codes and ‎quantum. [Online].; 2007 [cited 2020 6 19. Available from: ‎‎

‎4.‎ Emami M, Pedram L. Optimal linear codes over GF(7) and ‎GF(11) with dimension 3. Iranian Journal of Mathematical ‎Sciences and Informatics. 2015; 10(1): p. 11-22.‎

‎5.‎ González-Sarabia M, Rentería C. Generalized hamming weights ‎and some parameterized codes. Discrete Math. 2016; 339: p. ‎‎813-821.‎

‎6.‎ Johnsen T, Verdure H. Generalized Hamming weights for almost ‎affine codes. IEEE Trans. Inform. Theory. 2017; 63(4): p. 1941-‎‎1953.‎

‎7.‎ Halbawi W, Liu Z, Hassibi B. Balanced Reed-Solomon codes for ‎all parameters. In 2016 IEEE Information Theory Workshop ‎‎(ITW); 2016; Cambridge. p. 409-413.‎

‎8.‎ Tamo I, Barg A, Frolov A. Bounds on the parameters of locally ‎recoverable codes. IEEE Transactions on Information Theory. ‎‎2016; 62(6): p. 3070-3083.‎

‎9.‎ Yildiz H, Hassii B. Further Progress on the GM-MDS conjecture ‎for Reed-Solomon codes. In 2018 IEEE International Symposium ‎on Information Theory (ISIT); 2018; Vail, CO. p. 16-20.‎

‎10‎‎.‎ Heidarzadeh A, Sprintson A. 2017 IEEE International ‎Symposium on Information Theory (ISIT). 2017.‎

‎11‎‎.‎ Helleseth T. Projective codes meeting the Griesmer bound. ‎Discrete Mathematics. 1992; 106/107: p. 265-271.‎

‎12‎‎.‎ Hirschfeld JWP. Projective geometries over finite fields. 2nd ed. ‎New York: Ox- ford Mathematical Monographs, The Clarendon ‎Press, Oxford University Press; 1998. 576 p.‎