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Quantum synchronizable codes from repeated-root quasi-cyclic codes
Quantum synchronizable codes are generally constructed from cyclic codes. In this paper, we extend the class of codes available for constructing...
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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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An algebraic characterization of binary CSS-T codes and cyclic CSS-T codes for quantum fault tolerance
CSS-T codes were recently introduced as quantum error-correcting codes that respect a transversal gate. A CSS-T code depends on a CSS-T pair, which...
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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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On the duals of quasi-cyclic codes and their application to quantum codes
This paper presents some results on 1-generator quasi-cyclic (QC) codes and their duals over finite fields. We have explicitly obtained a set of...
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Quantum variations of cyclotomic cosets for cyclic stabiliser codes construction
Cyclotomic cosets are intrinsically linked with the design and construction of classical cyclic codes whose properties can be inferred from the coset...
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Finite field construction for quasi-cyclic LDPC convolutional codes with cyclic 2-D MDS codes
The parity-check matrices for quasi-cyclic low-density parity-check convolutional (QC-LDPC-C) codes have different characteristics of time-varying...
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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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A family of cyclic codes with two zeros
Cyclic codes have been applied in communication systems, data storage systems and consumer electronics widely. In this work, we explore q -ary cyclic...
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On construction of quantum codes with dual-containing quasi-cyclic codes
One of the main objectives of quantum error-correction theory is to construct quantum codes with optimal parameters and properties. In this paper, we...
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Two Families of Entanglement-Assisted Quantum Codes Constructed from Cyclic Codes
Entanglement-assisted quantum error-correcting (EAQEC) codes are a significant extension of quantum error-correcting codes. It has been found that an...
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New constructions of Sidon spaces and large cyclic constant dimension codes
Sidon spaces initially were introduced by Bachoc, Serra, and Zémor as a tool to characterize multiplicative properties of subspaces and...
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New binary and ternary quasi-cyclic codes with good properties
One of the most important and challenging problems in coding theory is to construct codes with best possible parameters and properties. The class of...
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New Binary Quantum Codes Constructed from Quasi-Cyclic Codes
It is well known that quantum codes can be constructed by means of classical symplectic dual-containing codes. This paper considers a family of...