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Obtaining new classes of optimal linear codes by puncturing and shortening optimal cyclic codes
In this paper we use the puncturing and shortening techniques on two already-known classes of optimal cyclic codes in order to obtain three new...
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Grassl–Rötteler cyclic and consta-cyclic MDS codes are generalised Reed–Solomon codes
We prove that the cyclic and constacyclic codes constructed by Grassl and Rötteler in International Symposium on Information Theory (ISIT), pp....
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Optimal quinary cyclic codes with three zeros
Cyclic codes are an important subclass of linear codes, they not only have good algebraic structure, but also are easy to be encoded and decoded. At...
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Some results on the Hamming distances of cyclic codes
Cyclic codes over finite fields have been studied for decades due to their wide applicability in communication systems, consumer electronics, and...
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Several classes of optimal cyclic codes with three zeros
As a class of linear codes, cyclic codes are widely used in communication systems, consumer electronics and data storage systems due to their...
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Private Information Retrieval Schemes Using Cyclic Codes
A Private Information Retrieval (PIR) scheme allows users to retrieve data from a database without disclosing to the server information about the...
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On the parameters of extended primitive cyclic codes and the related designs
Very recently, Heng et al. studied a family of extended primitive cyclic codes. It was shown that the supports of all codewords with any fixed...
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Several families of irreducible constacyclic and cyclic codes
In this paper, several families of irreducible constacyclic codes over finite fields and their duals are studied. The weight distributions of these...
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ℤ2ℤ4-Additive Cyclic Codes
Cyclic codes over finite fields are one of the most studied families of codes. They are a subfamily of linear codes and the process of codification...
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Cyclic constant dimension subspace codes via the sum of Sidon spaces
Subspace codes are of great use in noncoherent linear network coding (Katti et al in ACM SIGCOMM Comput Commun Rev 38(4):401–412, 2008; Kötter and...
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Generating Cyclic 2-Gray Codes for Fibonacci q-Decreasing Words
We present a two-stage algorithm for generating cyclic 2-Gray codes for q-decreasing words. In the first step, a simple recursive algorithm is used...
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Linear codes from support designs of ternary cyclic codes
For a long time, the literature has demonstrated that designs and codes are exciting topics for combinatorics and coding theory. Linear codes and t -de...
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A generalization of cyclic code equivalence algorithm to constacyclic codes
Recently, a new algorithm to test equivalence of two cyclic codes has been introduced which is efficient and produced useful results. In this work,...
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Three new classes of optimal quinary cyclic codes with minimum distance four
Due to their wide applications in consumer electronics, data storage systems and communication systems, cyclic codes have been an important subject...
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Symbol-pair weight distribution of some irreducible cyclic codes
In this paper, we study the symbol-pair weight distribution of some irreducible cyclic codes. We define generalized cyclotomic numbers and provide...