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The Sorting Index and Permutation Codes
permutation statistic Mahonian statistic Coxeter group set-valued statistic bijection
2014/6/3
In the combinatorial study of the coefficients of a bivariate polynomial that generalizes both the length and the reflection length generating functions for finite Coxeter groups, Petersen introduced ...
On non-existence of some (1,2)-optimal codes
Optimal codes Burst-error Parity-check matrix
2010/9/26
This paper presents the non-existence of certain blockwise burst error correcting (1,2)-Optimal linear codes over GF(q) (q is a prime) where the code length n is divided into two sub-blocks of lengths...
Iterative decoding of generalized parallel concatenated OSMLD codes
Parallel concatenated block codes OSMLD codes
2010/9/26
In this paper we well introduce a new decoding algorithm for generalized parallel concatenated block codes(GPCB). We are interested in decoding generalized parallel concatenated block codes based on t...
Codes correcting repeated burst errors blockwise
Error locating codes burst errors repeated burst errors
2010/9/27
This paper obtains bounds for linear codes which are capable to correct the errors blockwise which occur during the process of transmission. The kind of errors considered are known as repeated burst e...
Distributed Storage Codes with Repair-by-Transfer and Non-achievability of Interior Points on the Storage-Bandwidth Tradeoff
Repair-by-Transfer Non-achievability Interior Points Storage-Bandwidth Tradeoff
2010/11/17
Regenerating codes are a class of recently developed codes for distributed storage that, like Reed-Solomon codes, permit data recovery from any subset of k nodes within the n-node network. However, r...
Han's Bijection via Permutation Codes
Foata's second transformation Mahonian statistic cyclic major code cyclic inversion code partial Foata map
2014/6/3
We show that Han’s bijection when restricted to permutations can be carried out in terms of the cyclic major code and the cyclic inversion code. In other words, it maps a permutation π with cyclic maj...
In this paper, the subspace subcodes of generalized Reed-Solomn codes are codes are introduced and the fomulas to compute the dimensions of these codes are given.
ERROR DETECTION CAPABILITY OF SHORTENED HAMMING CODES AND THEIR DUAL CODES
Error detection undetected er
2007/12/11
The undetected error probability and error detection capability of shortened Hamming codes and their dual codes are studied in this paper. We also obtain some interesting properties for the shortened ...