
Weight Enumerators for NumberTheoretic Codes and Cardinalities of Nonbinary VT Codes
This paper investigates the extended weight enumerators for the numbert...
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Error correcting codes from subexceeding fonction
In this paper, we present errorcorrecting codes which are the results o...
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Learning a Code: Machine Learning for Approximate NonLinear Coded Computation
Machine learning algorithms are typically run on large scale, distribute...
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Unweighted linear congruences with distinct coordinates and the Varshamov–Tenengolts codes
In this paper, we first give explicit formulas for the number of solutio...
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Explicit Formulas for the Weight Enumerators of Some Classes of Deletion Correcting Codes
We introduce a general class of codes which includes several wellknown ...
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Idealtheoretic Explanation of Capacityachieving Decoding
In this work, we present an abstract framework for some algebraic error...
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Projective toric codes
Any integral convex polytope P in R^N provides a Ndimensional toric var...
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Distance Enumerators for NumberTheoretic Codes
The numbertheoretic codes are a class of codes defined by single or multiple congruences and are mainly used for correcting insertion and deletion errors. Since the numbertheoretic codes are generally nonlinear, the analysis method for such codes is not established enough. The distance enumerator of a code is a unary polynomial whose ith coefficient gives the number of the pairs of codewords with distance i. The distance enumerator gives the maximum likelihood decoding error probability of the code. This paper presents an identity of the distance enumerators for the numbertheoretic codes. Moreover, as an example, we derive the Hamming distance enumerator for the VarshamovTenengolts (VT) codes.
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