Non-malleable codes (NMCs), introduced by Dziembowski, Pietrzak and Wichs (ITCS 2010), provide a powerful guarantee in scenarios where the classical notion of error-correcting codes cannot provide any guarantee: a decoded message is either the same or completely independent of the underlying message, regardless of the number of errors introduced into the codeword. Informally, NMCs are defined with respect to a family of tampering functions F\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {F}$$\end{document} and guarantee that any tampered codeword decodes either to the same message or to an independent message, so long as it is tampered using a function f∈F\documentclass[12pt]{minimal}
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\begin{document}$$f \in \mathcal {F}$$\end{document}. One of the well-studied tampering families for NMCs is the t-split-state family, where the adversary tampers each of the t“states” of a codeword, arbitrarily but independently. Cheraghchi and Guruswami (TCC 2014) obtain a rate-1 non-malleable code for the case where t=O(n)\documentclass[12pt]{minimal}
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\begin{document}$$t = \mathcal {O}(n)$$\end{document} with n being the codeword length and, in (ITCS 2014), show an upper bound of 1-1/t\documentclass[12pt]{minimal}
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\begin{document}$$1-1/t$$\end{document} on the best achievable rate for any t-split state NMC. For t=10\documentclass[12pt]{minimal}
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\begin{document}$$t=10$$\end{document}, Chattopadhyay and Zuckerman (FOCS 2014) achieve a constant-rate construction where the constant is unknown. In summary, there is no known construction of an NMC with an explicit constant rate for any t=o(n)\documentclass[12pt]{minimal}
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\begin{document}$$t= o(n)$$\end{document}, let alone one that comes close to matching Cheraghchi and Guruswami’s lowerbound! In this work, we construct an efficient non-malleable code in the t-split-state model, for t=4\documentclass[12pt]{minimal}
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\begin{document}$$t=4$$\end{document}, that achieves a constant rate of 13+ζ\documentclass[12pt]{minimal}
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\begin{document}$$\frac{1}{3+\zeta }$$\end{document}, for any constant ζ>0\documentclass[12pt]{minimal}
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\begin{document}$$\zeta > 0$$\end{document}, and error 2-Ω(ℓ/logc+1ℓ)\documentclass[12pt]{minimal}
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\begin{document}$$2^{-\varOmega (\ell / log^{c+1} \ell )}$$\end{document}, where ℓ\documentclass[12pt]{minimal}
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\begin{document}$$\ell $$\end{document} is the length of the message and c>0\documentclass[12pt]{minimal}
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\begin{document}$$c > 0$$\end{document} is a constant.
