منابع مشابه
An Introduction to Linear and Cyclic Codes
We shall examine a small aspect of coding theory from an algebraic standpoint, examining the algorithms for decoding and encoding from a theoretical perspective. We assume basic knowledge of finite fields, but we shall introduce the theory of linear codes and built up to the machinery for generating cyclic codes and efficiently encoding and decoding them.
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For a linear code over GF (q) we consider two kinds of`subcodes' called residuals and punctures. When does the collection of residuals or punctures determine the isomorphism class of the code? We call such a code residually or puncture reconstructible. We investigate these notions of reconstruction and show that, for instance, selfdual binary codes are puncture and residually reconstructible. A...
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In the problem of blind reconstruction of channel codes, the receiver does not have the knowledge of the channel code used at the transmitter and the aim is to identify this unknown channel code corresponding to the given received sequence. In this paper, we study this blind reconstruction problem for binary cyclic codes. In the literature, several researchers have proposed blind reconstruction...
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An algebraic construction for constant dimension subspace codes is called orbit code. It arises as the orbits under the action of a subgroup of the general linear group on subspaces in an ambient space. In particular orbit codes of a Singer subgroup of the general linear group has investigated recently. In this paper, we consider the normalizer of a Singer subgroup of the general linear group a...
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Let GF (q) denote the Galois field of q elements, and let V (n, q) denote the vector space of all ordered n-tuples over GF (q). The number of nonzero positions in a vector x ∈ V (n, q) is called the Hamming weight wt(x) of x. The Hamming distance d(x,y) between two vectors x,y ∈ V (n, q) is defined by d(x,y) = wt(x − y). A linear code C of length n and dimension k over GF (q) is a k-dimensional...
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ژورنال
عنوان ژورنال: The Journal of Korea Information and Communications Society
سال: 2011
ISSN: 1226-4717
DOI: 10.7840/kics.2011.36c.10.605