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On the Griesmer bound for nonlinear codes

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 characterize a family of systematic nonlinear codes for which the Griesmer bound holds. 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 (weaker) versions of the Griesmer bound holding for all systematic codes.

preprint2015arXivOpen access
Emanuele BelliniEleonora GuerriniAlessio MeneghettiMassimiliano Sala
math.COmath.ITInformation Theory
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Open access4 authors3 topics
Imported metadata coverageMissing code, dataset, citation and institution fields are tracked without dominating the paper.Details
Citations: 0Reviews: 0Saves: 0Code: not linkedDataset: not linkedInstitutions: 0

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Emanuele BelliniEleonora GuerriniAlessio MeneghettiMassimiliano Sala

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