A) , (L J regular QC-LDPC code of length N is defined by a parity-check matrix L L p I p I p I p I p I p I p I p I p I H     (1) where 1 1    J j , 1 1    L l and   l j p I , represents the p p  circulant permutation matrix obtained by cyclically right-shifting the p p  identity matrix   0 I by l j p , positions, with. / L N p  For a specific QC-LDPC code we define the correspo...

The rank modulation scheme has been proposed for efficient writing and storing data in non-volatile memory storage. Error-correction in the rank modulation scheme is done by considering permutation codes. In this paper we consider codes in the set of all permutations on n elements, Sn, using the Kendall’s τ -metric. We prove that there are no perfect single-error-correcting codes in Sn, where n...

A quasi-cyclic (QC) low-density parity-check (LDPC) code can be viewed as the protograph code with circulant permutation matrices. In this paper, we find all the subgraph patterns of protographs of QC LDPC codes having inevitable cycles of length 2i, i = 6, 7, 8, 9, 10, i.e., the cycles existing regardless of the shift values of circulants. It is also derived that if the girth of the protograph...

The rank modulation scheme has been proposed for efficient writing and storing data in non-volatile memory storage. Error-correction in the rank modulation scheme is done by considering permutation codes. In this paper we consider codes in the set of all permutations on n elements, Sn, using the Kendall’s τ -metric. We prove that there are no perfect single-error-correcting codes in Sn, where n...

We propose a PMAC-type mode of operation that can be used as a highly secure MAC (Message Authentication Code) or PRF (Pseudo-Random Function). Our scheme is based on the assumption that the underlying n-bit blockcipher is a pseudo-random permutation. Our construction, which we call PMAC Plus, involves extensive modification to PMAC, requiring three blockcipher keys. The PMAC Plus algorithm is ...

We solve by a genetic algorithm (GA), three NPhard, constrained, minimal spanning tree (MST) problems on a complete graph using a novel encoding for the genotype which ensures feasibility of the search space when performing crossover and mutation and when initializing the population. By employing a feasible encoding the standard, mainstream, GA paradigm is preserved allowing us to capture the f...

The Z p 2 -additive codes are subgroups of α 1 × , and can be seen as linear over when = 0 or 4 . A -linear generalized Hadamard (GH) code is a GH which the Gray map image code. In this paper, we generalize some known results for with to any ≥ 3 prime ≠ First, give recursive construction type ( ; t ) We also present many different constructions having same type, show that obtain permutation equ...

9 10 11 Caserta, R. ; Takita, M. A.; Targon, M. L.; Rosselli-Murai, L. K.; de Souza, A. P.; Peroni, L.; Stach-Machado, D. R.; Andrade, A.; Labate, C. A.; Kitajima, E. W.; Machado, M.A.; de Souza, A. A. 1. Centro APTA Citros Sylvio Moreira/IAC, Rodovia Anhanguera Km 158, Cordeirópolis – 7 SP, BRAZIL, Zip code: 13490-970. 8 2. Universidade Estadual de Campinas/UNICAMP, Centro de Biologia Molecula...

We demonstrate the first attacks on the SPN ciphers with 6, 7, 8, and 9 secret layers. In particular, we show a decomposition attack on the SASASASAS scheme when the S-box size m and the block length n satisfy the condition m ≤ n (for example, 8-bit S-box and 128-bit block).

Interleavers are important blocks of the turbo codes, their types and dimensions having a significant influence on the performances of the mentioned codes. If appropriately chosen, the permutation polynomial (PP) based interleavers lead to remarkable performances of these codes. The most used interleavers from this category are quadratic permutation polynomials (QPPs) and cubic permutation poly...