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We propose an algorithm which is an improved version of the KabatianskyTavernier list decoding algorithm for the second order Reed-Muller code RM(2, m), of length n = 2 m , and we analyse its theoretical and practical complexity. This improvement allows a better theoretical complexity. Moreover, we conjecture another complexity which corresponds to the results of our simulations. This algorithm has the strong property of being deterministic and this fact drives us to consider some applications, like determining some lower bounds concerning the covering radius of the RM(2, m) code. AMS Classifications94B05 · 94B35 · 94B65 · 94A60 IntroductionIntroduced by Elias [1] 50 years ago, the concept of list decoding has been recently revived thanks to Sudan's discovery [2] of efficient list decoding algorithms for Reed-Solomon (RS) codes. Despite that there are similarities between Reed-Solomon and Reed-Muller (RM) codes, no efficient list decoding algorithm for RM codes was known until very recently. This article is a rewritten and completed version of Fourquet R., Tavernier C.: List decoding of second order Reed-Muller codes and its covering radius implications, Workshop on Coding and Cryptography 2007, pp. 147-156. R. Fourquet (B)

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The sense of touch provides a particular access to our environment, enabling a tangible relation with it. In the particular case of cultural heritage, touching the past, apart from being a universal dream, can provide essential information to analyze, understand, or restore artifacts. However, archaeological objects cannot always offer tangible access, either because they have been destroyed or are too damaged, or because they are part of a larger assembly. In other cases, it is the context of use that has become inaccessible, as it is related to an outdated activity. We propose a workflow based on a combination of computed tomography, 3D images, and 3D printing to provide concrete access to cultural heritage, and we illustrate this workflow in different contexts of inaccessibility. These technologies are already used in cultural heritage, but seldom combined, and are most often employed for exceptional artifacts. We propose to combine these technologies in case studies corresponding to relevant archaeological situations.