Weight Distribution of Some Codewords of 3-ary Linear Code over GF(27)
Keywords:Finite projective space, Incidence matrix, linear code, Weight distribution.
This paper is devoted to introduce the structure of the p-ary linear codes C(n,q) of points and lines of PG(n,q),q=p^h prime. When p=3, the linear code C(2,27) is given with its generator matrix and also, some of weight distributions are calculated.
E F Assmus and J D Key, Designs and their codes. Cambridge; New York, USA: Cambridge University Press, 1992. ISBN-13: 978-0521413619.
B Bagchi and S P Inamdar , "Projective geometric codes," Journal of Combinatorial Theory, Series A, vol. 99, no. 1, pp. 128-142, 2002.
B A Dubrovin , A T Fomenko, and S P Novikov, Modern geometry methods and application: Part 1. The geometry of surfaces, transformation groups, and fields. New York: Springer Verlag, 1985. ISBN-13: 978-0387976631.
F J MacWilliams and NJ A Sloane, The Theory of error-correcting codes, 6th ed. Amsterdam: North-Holland Publishing Company, 1977. ISBN: 0 444 85009 0.
J W P Hirschfeld, Projective geometries over finite fields, 2nd ed. New York: Ox- ford Mathematical Monographs, The Clarendon Press, Oxford University Press, 1998. ISBN: 9780198502951.
O Olmez, "A link between combinatorial designs and three-weight linear codes," Designs Codes and Cryptography, vol. 86, no. 9, pp. 1-17, 2017.
C. Ding, C. Li, N. Li and Z. Zhou, "Three-weight cyclic codes and their weight distributions," Discrete Mathematics, vol. 339, no. 2, pp. 415-427, 2016.
L Gaojun, X Cao, S Xu, and J Mi, "Binary linear codes with two or three weights from niho exponents," Cryptography and Communications, vol. 10, no. 2, pp. 301-318, 2018.
C Li, Q Yue, and F Fu, "A construction of several classes of two-weight and threeweight linear codes," Applicable Algebra in Engineering Communication and Computing, vol. 28, no. 1, pp. 1-20, 2018.
Y W Liu and Z H Liu, "On some classes of codes with a few weights," Adv. Math. Commun., pp. 415-428, 2018.
S Yang, Z Yao, and C Zhao, "The weight distributions of two classes of p-ary cyclic codes with few weights," Finite Fields and Their Applications, vol. 44, pp. 76-91, 2017.
The GAP Group. (2020) GAP. Reference manual.
How to Cite
Articles accepted for publication in Al-Mustansiriyah Journal of Science (MJS) are protected under the Creative Commons Attribution 4.0 International License (CC BY-NC). Authors of accepted articles are requested to sign a copyright release form prior to their article being published. All authors must agree to the submission, sign copyright release forms, and agree to be included in any correspondence between MJS and the authors before submitting a work to MJS. For personal or educational use, permission is given without charge to print or create digital copies of all or portions of a MJS article. However, copies must not be produced or distributed for monetary gain. It is necessary to respect the copyright of any parts of this work that are not owned by MJS.