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...Contemporary algebraic and geometric techniques in coding theory cryptography summer school july universit a degli studi della campania luigi vanvitelli the matrix code equivalence problem applications krijn reijnders simona samardjiska monika trimoska affiliation radboud university netherlands abstract amatrix is subspace c of m n matrices over fq endowed with rank metric defined as d b we de note by k dimension f its basis q where fm are linearly independent since their i introduction loo keng hu error correcting codes have found various domains such network space time public key grow ing interest latter domain due to urgent necessity cryptographic community find explore problems that hard solve even for an attacker has access quantum computer thesecurityofclassical contrast post cryp tography based on hardness factorisation discrete log both which can be solved polynomial using shor s algorithm thus building crypto graphic schemes need one way functions easy compute classical but in...