Geodesic
Classification of Hadamard productsof one-codimensional subcodesof Reed--Muller codes
Diskretnaya Matematika, Tome 32 (2020) no. 1, pp. 115-134

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For Reed–Muller codes we consider subcodes of codimension 1. A classification of Hadamard products of such subcodes is obtained. With the use of this classification it has been shown that in most cases the problem of recovery of the secret key of a code-based cryptosystem employing such subcodes is equivalent to the problem of recovery of the secret key of the same cryptosystem based on Reed–Muller codes, which is known to be tractable.
Keywords: McEliece public key cryptosystem, code-based cryptosystems, Reed–Muller codes, cryptanalysis, Hadamard product, square of a code, classification of Hadamard products, subcodes of codimension 1. 
@article{DM_2020_32_1_a8,
     author = {I. V. Chizhov and M. A. Borodin},
     title = {Classification of {Hadamard} productsof one-codimensional subcodesof {Reed--Muller} codes},
     journal = {Diskretnaya Matematika},
     pages = {115--134},
     publisher = {mathdoc},
     volume = {32},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2020_32_1_a8/}
}
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I. V. Chizhov; M. A. Borodin. Classification of Hadamard productsof one-codimensional subcodesof Reed--Muller codes. Diskretnaya Matematika, Tome 32 (2020) no. 1, pp. 115-134. http://geodesic.mathdoc.fr/item/DM_2020_32_1_a8/