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On the Griesmer bound for nonlinear codes

Abstract : Most bounds on the size of codes hold for any code, whether linear or nonlinear. Notably, the Griesmer bound holds only in the linear case. In this paper we identify code parameters (q, d, k) for which the Griesmer bound holds also in the (systematic) nonlinear case. Moreover, we show that the Griesmer bound does not necessarily hold for a systematic code by showing explicit counterexamples. On the other hand, we are also able to provide some versions of the Griesmer bound holding for all systematic codes.
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https://hal.inria.fr/hal-01276224
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Submitted on : Friday, February 19, 2016 - 8:11:33 AM
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Emanuele Bellini, Alessio Meneghetti. On the Griesmer bound for nonlinear codes. WCC2015 - 9th International Workshop on Coding and Cryptography 2015, Anne Canteaut, Gaëtan Leurent, Maria Naya-Plasencia, Apr 2015, Paris, France. ⟨hal-01276224⟩

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