Weight Distribution of Some Codewords of 3-ary Linear Code over GF(27)
DOI:
https://doi.org/10.23851/mjs.v31i4.906Keywords:
Finite projective space, Incidence matrix, linear code, Weight distribution.Abstract
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.
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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.
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