On Optimal Nonlinear Systematic Codes

Abstract : Most bounds on the size of codes hold for any code, whether linear or not. Notably, the Griesmer bound holds only in the linear case and so optimal linear codes are not necessarily optimal codes. In this paper, we identify code parameters (q,d,k) , namely, field size, minimum distance, and combinatorial dimension, for which the Griesmer bound also holds in the (systematic) nonlinear case. Moreover, we show that the Griesmer bound does not necessarily hold for a systematic code by explicit construction of a family of optimal systematic binary codes. On the other hand, we are able to provide some versions of the Griesmer bound holding for all the systematic codes.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-01325813
Contributor : Eleonora Guerrini <>
Submitted on : Thursday, June 2, 2016 - 4:51:55 PM
Last modification on : Thursday, July 5, 2018 - 3:28:39 PM

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Eleonora Guerrini, Alessio Meneghetti, Massimiliano Sala. On Optimal Nonlinear Systematic Codes. IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2016, 62 (6), pp.3103-3112. ⟨10.1109/TIT.2016.2553142⟩. ⟨lirmm-01325813⟩

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