Abstract
This paper is devoted to the construction of one-Lee weight codes and two-Lee weight codes over F p + vF p (v 2 = v) with type \({p^{2{k_1}}}{p^{{k_2}}}{p^{{k_3}}}\) based on two different distance-preserving Gray maps from ((F p + vF p )n, Lee weight) to (F 2n p , Hamming weight), where p is a prime. Moreover, the authors prove that the obtained two-Lee weight codes are projective only when p = 2.
Similar content being viewed by others
References
Bonisoli A, Every equidistant linear code is a sequence of dual Hamming codes, Ars. Combin., 1984, 18: 181–186.
Lint J V and Tolhuizenon L, On perfect ternary constant weight codes, Des. Codes Cryptogr., 1999, 18(1–3): 231–234.
Carlet C, One-weight Z4-linear codes, Coding Theory, Cryptography and Related Areas, Springer, 2000, 57–72.
Wood J A, The structure of linear codes of constant weight, Trans. Amer. Math. Soc., 2001, 354(3): 1007–1026.
Shi M J, Optimal p-ary codes from one-weight linear codes over zpm, Chinese Journal of Electronics, 2013, 22(4): 799–802.
Shi M J, Zhu S X, and Yang S L, A class of optimal p-ary codes from one-weight codes over Fp[u]/<u m>, J. Frank. Inst., 2013, 350(5): 929–937.
Van Lint J H and Schrijver A, Construction of strongly regular graphs, two-weight codes and partial geometries by finite fields, Combinatorica, 1981, 11(1): 63–73.
Bouyukliev I, Fack V, Willems W, et al., Projective two-weight codes with small parameters and their corresponding graphs, Des. Codes Cryptogr., 2006, 41(1): 59–78.
Brouwer A E and Eupen M V, The correspondence between projective codes and 2-weight codes, Des. Codes Cryptogr., 1997, 11(3): 261–266.
Calderbank R and Kantor W M, The geometry of two-weight codes, Bull. London Math. Soc, 1986, 18(2): 97–122.
Ling S and Solé P, Two-weight codes over chain rings and partial difference sets, Rapport de recherche I3S/RR-2002-40FR, http://www.i3s.unice.fr/I3S/FR.
Yuan J and Ding C S, Secret sharing schemes from two-weight codes. R. C. Bose Centenary Symposium on Discrete Mathematics and Applications, Indian Statistical Institute, Kolkata, India, 2002, 20–23.
Shi M J and Chen L, Construction of two-Lee weight codes over Fp + vFp + v2Fp, International Journal of Computer Mathematics, 2016, 93(3): 415–424.
Shi M J and Solé P, Optimal p-ary codes from one-weight codes and two-weight codes over Fp + vFp, Journal of Systems Science and Complexity, 2015, 28(3): 679–690.
Zhu S X and Wang L Q, A class of constacyclic codes over Fp +vFp and its Gray image, Discrete Math., 2011, 311(23): 2377–2682.
Zhu S X, Wang Y, and Shi M J, Some results on cyclic codes over F2+vF2, IEEE Trans. Inform. Theory, 2010, 56(4): 1680–1684.
Ling S and Xing C P, Coding Theory — A First Course, Cambridge University Press, Cambridge, 2004, 83–95.
Author information
Authors and Affiliations
Corresponding author
Additional information
This research was supported by the National Natural Science Foundation of China under Grant No. 61202068, Technology Foundation for Selected Overseas Chinese Scholar, Ministry of Personnel of China under Grant No. 05015133, the Open Research Fund of National Mobile Communications Research Laboratory, Southeast University under Grant No. 2015D11, and Key Projects of Support Program for Outstanding Young Talents in Colleges and Universities under Grant No. gxyqZD2016008.
This paper was recommended for publication by Editor ZHANG Zhifang.
Rights and permissions
About this article
Cite this article
Shi, M., Luo, Y. & Solé, P. Construction of one-Lee weight and two-Lee weight codes over F p + vF p . J Syst Sci Complex 30, 484–493 (2017). https://doi.org/10.1007/s11424-016-5062-z
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11424-016-5062-z