Binary and Gray codes for integers 0–15
Gray codes and symmetric chains
... Introduction Gray codes are named after Frank Gray, a researcher at Bell Labs, who described a simple method to generate all 2 n bitstrings of length n by flipping a single bit in each step [8], now ...
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Improved Methods For Generating Quasi-Gray Codes
... a Gray code remains ...standard binary representations of 0 to 2 d − 1, in the worst case, will require reading and writing all d bits to generate the next bit string, but it may also read and write ...
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Spatial Image Watermarking by Error Correction Coding in Gray Codes
... the Gray-ECC method is superior to that of the ECC in natural binary codes for changes in signal ...the Gray-ECC method were conducted on 8-bit monochrome images to evaluate both the features ...
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A Secure Encryption Through Gray Codes And BigIntegers For IoT Devices
... weighted codes, each successive digit from right to left represents weights equal to some specified value and to get the equivalent decimal number system we sum the products of these weights by the corresponding ...
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Codes over Quaternion Integers
... Block codes, Mannheim distance, Cyclic codes, Syndrome decoding ...consider codes over finite fields equipped with a quaternion Mannheim ...and codes over Gaussian integers with respect ...
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Optimal, Divisible binary Codes from Gray-Homogeneous Images of Codes over R_{k,m}
... Reed-Muller codes to find a distance-preserving map that takes codes over R k,m to binary ...quasicyclic codes over R k,m of different lengths for different values of k and m, we construct a ...
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On Binary Signed Digit Representations of Integers
... = 0, where t is the number of 0s to be written to the output for that group as ...to 0, the two possible alternatives at the group boundary are considered as was explained in Section ...to 0 ...
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Binary Codes and Caps
... between codes and caps have been well studied (see for example [1], [4 –6], ...such codes C using Theorem ...any binary linear code with d = 4 is either a quasi-perfect code or a shortening of some ...
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Binary codes are suitable for the computer applications. Binary codes are suitable for the digital communications.
... 4- Binary Codes This section describes various popular Binary Code ...of binary bits. This group is also called as binary code. The binary code is represented by the number as ...
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The four [10,5,4] binary codes
... 3 5 : The …rst three columns are at the support of b 1 and the second three support b 2 . Any codeword c must have an even number of 1s in each of these supports to give b 1 c = b 2 c = 0. The sum of the three 8s ...
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On the Concatenations of Polar Codes and Non-binary LDPC Codes
... binary outer code has the potential to match better with multibit-decision approach which can significantly reduce latency of traditional SCL decoders [16, 17]. 2) A new decoding scheme, named selective extended ...
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The Influence of Binary Representations of Integers on the Performance of Selectorecombinative Genetic Algorithms
... different binary representations of integers influences the performance of selectorecombinative GAs using only crossover and no ...The binary and gray encoding are two different, well known ...
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Efficient computation of middle levels Gray codes
... levels Gray code is a cyclic listing of all bitstrings of length 2n+1 that have either n or n+1 entries equal to 1 such that any two consecutive bitstrings in the list differ in exactly one ...a Gray code ...
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Codes over integers, and the singularity of random matrices with large entries
... MDS codes and the alphabet size needed to realize them over ...the integers) of the same dimensions as P , is said to realize P if it satisfies the following two ...
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Sequential Decoding of Binary Convolutional Codes
... [9] D. Haccoun and M. J. Ferguson, Generalized stack algorithms for decoding convolutional codes IEEE Trans. Inform. Theory, vol. IT-21, no. 6, pp. 638–651, November 1975. [10] Y. S. Han, P.-N. Chen, and M. P. C. ...
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Construction of Some Binary LCD Codes
... trivially. Binary LCD codes play a significant role for their advantage of low complexity for implementations against side-channel ...LCD codes over F 2 by puncturing, shortening and ...cyclic ...
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Multi non binary turbo codes
... turbo codes called multi-non-binary turbo codes (MNBTCs) that generalizes the concept of turbo codes to multi-non-binary (MNB) parallel concatenated convolutional codes ...turbo ...
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Blind recognition of binary cyclic codes
... Cyclic codes are one class of the most important error-correcting codes ap- plied in communication ...the codes and modulations are usually known by the transmitters and receivers ...
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Study of Some Bounds on Binary Codes
... Then these bounds are studied with example and various types of upper bounds are calculated for size and distance. The comparison of these bounds have been done and the tighter bounds for ( , ) is discussed. Keywords: ...
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Gray Codes for Set Partitions and Restricted Growth Tails
... We survey results on generating set partitions, S( n), and restricted growth tails, T( n, k), with an emphasis on Gray code listings, in which the change be- tween succes[r] ...
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