Perfect binary codes: classification and properties
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Properties of perfect transitive binary codes of length 15 and extended perfect transitive binary codes of length 16
Properties of perfect transitive binary codes of length 15 and extended perfect transitive binary codes of length 16 Abstract. Some properties of perfect transitive binary codes of length 15 and extended perfect transitive binary codes of length 16 are presented for reference purposes. The attached files contain some tab-delimited properties of perfect binary codes of length 15 and extended per...
متن کاملPerfect codes and related topics
The topic of perfect codes is one of the most important topics in the theory of error-correcting codes. The class of perfect codes is very complicated, large (double exponential) and intensively studied by many researches. The investigation of nontrivial properties of perfect codes is significant both from coding point of view (for the solution of the classification problem for such codes) and ...
متن کاملThe Perfect Binary One-Error-Correcting Codes of Length 15: Part II--Properties
A complete classification of the perfect binary oneerror-correcting codes of length 15 as well as their extensions of length 16 was recently carried out in [P. R. J. Östergård and O. Pottonen, “The perfect binary one-error-correcting codes of length 15: Part I—Classification,” submitted for publication]. In the current accompanying work, the classified codes are studied in great detail, and the...
متن کاملThe (non-)existence of perfect codes in Lucas cubes
A Fibonacci string of length $n$ is a binary string $b = b_1b_2ldots b_n$ in which for every $1 leq i < n$, $b_icdot b_{i+1} = 0$. In other words, a Fibonacci string is a binary string without 11 as a substring. Similarly, a Lucas string is a Fibonacci string $b_1b_2ldots b_n$ that $b_1cdot b_n = 0$. For a natural number $ngeq1$, a Fibonacci cube of dimension $n$ is denoted by $Gamma_n$ and i...
متن کاملPerfect binary codes: constructions, properties, and enumeration
Properties of nonlinear perfect binary codes are investigated and several new constructions of perfect codes are derived from these properties. An upper bound on the cardinality of the intersection of two perfect codes of length n is presented, and perfect codes whose intersection attains the upper bound are constructed for all n. As an immediate consequence of the proof of the upper bound we o...
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تاریخ انتشار 2009