Results 281 to 290 of about 5,134,174 (310)
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Computing Linear Codes and Unitals
Designs, Codes and Cryptography, 1998A unital on \(q^3+1\) points is a 2-\((q^3+1,q+1,1)\) design. The Ree unital \(R(q)\) on \(q^3+1\) points for \(q=3^{2m+1}\), \(m\geq 0\) is a design invariant under the Ree group. In 1981, Andries Brouwer constructed 138 nonisomorphic 2-\((28,42,1)\) designs and made the conjecture that the Ree unital \(R(3)\) is characterized by the fact that its ...
David B. Jaffe, Vladimir D. Tonchev
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Extendability of Ternary Linear Codes
Designs, Codes and Cryptography, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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An Extension Theorem for Linear Codes
Designs, Codes and Cryptography, 1999The author gives a simple sufficient condition for the existence of an extension of an \([n,k,d]_q\) code (with \((d,q)=1\)) to an \([n+1,k,d+1]_q\) code: if the weights of the code are all congruent to \(0\) or \(d\) modulo \(q\) then the code can be extended and the weights of the new code are all congruent to \(0\) or \(d+1\) modulo \(q\). The proof
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On the Concatenated Structure of a Linear Code
Applicable Algebra in Engineering, Communication and Computing, 1998Let \(F_q\) be a finite field with \(q\) elements and denote by \(C(n,k,d)\) a linear code of length \(n\) over \(F_q\) of dimension \(k\) and minimum distance \(d\). Define \(B(n_B,k_B,d_B)\) over \(F_q\) to be an inner code, \(E(n_E,k_E,d_E)\) over \(F_{q^{k_B}}\) to be an outer code and \({\mathcal C}\) to be the concatenateed code, obtained by ...
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Australas. J Comb., 1993
We give an algebraic characterization of weight functions on linear codes, i.e. vector spaces of \(n\)-tuples over a finite field. Specifically, given a function from a finite vector space \(V\) to the nonnegative integers, we determine precisely when \(V\) can be replaced (isomorphically) by a space of \(n\)-tuples so that the given function becomes ...
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We give an algebraic characterization of weight functions on linear codes, i.e. vector spaces of \(n\)-tuples over a finite field. Specifically, given a function from a finite vector space \(V\) to the nonnegative integers, we determine precisely when \(V\) can be replaced (isomorphically) by a space of \(n\)-tuples so that the given function becomes ...
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Forcing Linearity on Greedy Codes
Designs, Codes and Cryptography, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Summary: Because of their practical significance linear block codes are traditionally included in basic Coding Theory courses. In this paper, using a rich set of simple examples, we demonstrate some interesting facts which, we believe, are useful to get to know for students, and will help them to learn how to solve practical error control problems in ...
Baicheva, Tsonka +3 more
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Baicheva, Tsonka +3 more
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A Subfield-Based Construction of Optimal Linear Codes Over Finite Fields
IEEE Transactions on Information Theory, 2022Xiaohu Tang, Xiangyong Zeng, Nian Li
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