20,179 research outputs found
Cyclic unequal error protection codes constructed from cyclic codes of composite length
The distance structure of cyclic codes of composite length was investigated. A lower bound on the minimum distance for this class of codes is derived. In many cases, the lower bound gives the true minimum distance of a code. Then the distance structure of the direct sum of two cyclic codes of composite length were investigated. It was shown that, under certain conditions, the direct-sum code provides two levels of error correcting capability, and hence is a two-level unequal error protection (UEP) code. Finally, a class of two-level UEP cyclic direct-sum codes and a decoding algorithm for a subclass of these codes are presented
Some Results on the Weight Structure of Cyclic Codes of Composite Length
In this work we investigate the weight structure of cyclic codes of composite length n = n1n2, where n1 and n2 are relatively prime. The actual minimum distances of some classes of binary cyclic codes of composite length are derived. For other classes new lower bounds on the minimum distance are obtained. These new lower bounds improve on the BCH bound for a considerable number of binary cyclic codes
A Study on the Impact of Locality in the Decoding of Binary Cyclic Codes
In this paper, we study the impact of locality on the decoding of binary
cyclic codes under two approaches, namely ordered statistics decoding (OSD) and
trellis decoding. Given a binary cyclic code having locality or availability,
we suitably modify the OSD to obtain gains in terms of the Signal-To-Noise
ratio, for a given reliability and essentially the same level of decoder
complexity. With regard to trellis decoding, we show that careful introduction
of locality results in the creation of cyclic subcodes having lower maximum
state complexity. We also present a simple upper-bounding technique on the
state complexity profile, based on the zeros of the code. Finally, it is shown
how the decoding speed can be significantly increased in the presence of
locality, in the moderate-to-high SNR regime, by making use of a quick-look
decoder that often returns the ML codeword.Comment: Extended version of a paper submitted to ISIT 201
Functional diagnosability and recovery from massive faults in digital systems Quarterly progress reports, 17 May - 16 Nov. 1970 /final/
Diagnosability and recovery from massive faults in digital system
Transitive and self-dual codes attaining the Tsfasman-Vladut-Zink bound
A major problem in coding theory is the question of whether the class of cyclic codes is asymptotically good. In this correspondence-as a generalization of cyclic codes-the notion of transitive codes is introduced (see Definition 1.4 in Section I), and it is shown that the class of transitive codes is asymptotically good. Even more, transitive codes attain the Tsfasman-Vladut-Zink bound over F-q, for all squares q = l(2). It is also shown that self-orthogonal and self-dual codes attain the Tsfasman-Vladut-Zink bound, thus improving previous results about self-dual codes attaining the Gilbert-Varshamov bound. The main tool is a new asymptotically optimal tower E-0 subset of E-1 subset of E-2 subset of center dot center dot center dot of function fields over F-q (with q = l(2)), where all extensions E-n/E-0 are Galois
Stabilizer codes from modified symplectic form
Stabilizer codes form an important class of quantum error correcting codes
which have an elegant theory, efficient error detection, and many known
examples. Constructing stabilizer codes of length is equivalent to
constructing subspaces of which are
"isotropic" under the symplectic bilinear form defined by . As a
result, many, but not all, ideas from the theory of classical error correction
can be translated to quantum error correction. One of the main theoretical
contribution of this article is to study stabilizer codes starting with a
different symplectic form.
In this paper, we concentrate on cyclic codes. Modifying the symplectic form
allows us to generalize the previous known construction for linear cyclic
stabilizer codes, and in the process, circumvent some of the Galois theoretic
no-go results proved there. More importantly, this tweak in the symplectic form
allows us to make use of well known error correcting algorithms for cyclic
codes to give efficient quantum error correcting algorithms. Cyclicity of error
correcting codes is a "basis dependent" property. Our codes are no more
"cyclic" when they are derived using the standard symplectic forms (if we
ignore the error correcting properties like distance, all such symplectic forms
can be converted to each other via a basis transformation). Hence this change
of perspective is crucial from the point of view of designing efficient
decoding algorithm for these family of codes. In this context, recall that for
general codes, efficient decoding algorithms do not exist if some widely
believed complexity theoretic assumptions are true
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