Abstract
Certain equivalent conditions are given for the equivalence of linear codes using the properties of the relative subcodes derived from the relative generalized Hamming weight.
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Assmus E.F., Mattson H.F.: Error-correcting codes: an axiomatic approach. Inform. Contr. 6, 315–330 (1963)
Bogart K., Goldberg D., Gordon J.: An elementary proof of the MacWilliams theorem on equivalence of codes. Inform. Contr. 37, 19–22 (1978)
Chen W.D., Kløve T.: The weight hierarchies of q-ary codes of dimension 4. IEEE Trans. Inform. Theory 42, 2265–2272 (1996)
Fan Y., Liu H.W., Puig L.: Generalized Hamming weights and equivalences of codes. Sci. China 46, 690–695 (2003)
Kelly L., Bierbrauer J., Bierbrauer B.: Introduction to Coding Theory. Chapman, Hall/CRC, Boca Raton (2005)
Liu Z.H., Chen W.D., Luo Y.: The relative generalized Hamming weight of linear q -ary codes and their subcodes. Des. Codes Cryptogr. 48, 111–123 (2008)
Luo Y., Chaichana M., Han Vinck A.J., Chen K.F.: Some new characters on the wire-tap channel of type II. IEEE Trans. Inform. Theory 51, 1222–1229 (2005)
MacWilliams, F.J.: Combinatorial properties of elementary abelian groups. Ph.D. thesis, Radcliffe College, Cambridge, Mass. (1962)
Ward H.N., Wood J.A.: Characters and the equivalence of codes. J. Combin. Theory Ser. A 73, 348–352 (1996)
Wei V.K.: Generalized Hamming weight for linear codes. IEEE Trans. Inform. Theory 37, 1412–1418 (1991)
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This work was supported by the Special Training Program of Beijing Institute of Technology.
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Liu, Z., Sun, Z. On the equivalence of linear codes. AAECC 22, 137–145 (2011). https://doi.org/10.1007/s00200-011-0142-8
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DOI: https://doi.org/10.1007/s00200-011-0142-8