Martianus Frederic Ezerman

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We solve an open question in code-based cryptography by introducing the first provably secure group signature scheme from codebased assumptions. Specifically, the scheme satisfies the CPA-anonymity and traceability requirements in the random oracle model, assuming the hardness of the McEliece problem, the Learning Parity with Noise problem, and a variant of(More)
The weights in maximum distance separable (MDS) codes of length n and dimension k over the finite field GF(q) are studied. Up to some explicit exceptional cases, the MDS codes with parameters given by the MDS conjecture are shown to contain all k weights in the range n - k + 1 to n. The proof uses the covering radius of the dual code.
We introduce an additive but not F4-linear map S from Fn4 to F 4 and exhibit some of its interesting structural properties. If C is a linear [n, k, d]4-code, then S(C) is an additive (2n, 2 , 2d)4-code. If C is an additive cyclic code then S(C) is an additive quasi-cyclic code of index 2. Moreover, if C is a module θ-cyclic code, a recently introduced type(More)
Asymmetric quantum error-correcting codes (AQCs) may offer some advantage over their symmetric counterparts by providing better error-correction for the more frequent error types. The well-known CSS construction of q-ary AQCs is extended by removing the F<sub>q</sub>-linearity requirement as well as the limitation on the type of inner product used. The(More)
Using the Calderbank-Shor-Steane (CSS) construction, pure q-ary asymmetric quantum error-correcting codes attaining the quantum Singleton bound are constructed. Such codes are called asymmetric quantum maximum distance separable (AQMDS) codes. Assuming the validity of the MDS Conjecture, pure CSS AQMDS codes of all possible parameters are accounted for.
A class of powerful q-ary linear polynomial codes originally proposed by Xing and Ling is deployed to construct good asymmetric quantum codes via the standard CSS construction. Our quantum codes are q-ary block codes that encode k qudits of quantum information into n qudits and correct up to b(dx−1)/2c bit-flip errors and up to b(dz−1)/2c phase-flip(More)
We propose a construction of de Bruijn sequences by the cycle joining method from linear feedback shift registers (LFSRs) with arbitrary characteristic polynomial f(x). We study in detail the cycle structure of the set Ω(f(x)) that contains all sequences produced by a specific LFSR on distinct inputs and provide an efficient way to find a state of each(More)