arXiv subjects

Ruihu Li

Publications and source records attributed to Ruihu Li.

23 records · Page 2Linked to original sources

arXiv2018

Entanglement-assisted quantum MDS codes from constacyclic codes with large minimum distance

The entanglement-assisted (EA) formalism allows arbitrary classical linear codes to transform into entanglement-assisted quantum error correcting codes (EAQECCs) by using pre-shared entanglement between the sender and the receiver. In this work, we propose a decomposition of the defining set of constacyclic codes. Using this method, we construct four classes of $q$-ary entanglement-assisted quantum MDS (EAQMDS) codes based on classical constacyclic MDS codes by exploiting less pre-shared maximally entangled states. We show that a class of $q$-ary EAQMDS have minimum distance upper limit greater than $3q-1$. Some of them have much larger minimum distance than the known quantum MDS (QMDS) codes of the same length. Most of these $q$-ary EAQMDS codes are new in the sense that their parameters are not covered by the codes available in the literature.

cs.IT↗

arXiv2018

Some binary BCH codes with length $n=2^m+1$

Under research for near sixty years, Bose-$\!$Ray-$\!$Chaudhuri-$\!$Hocquenghem(BCH) codes have played increasingly important roles in many applications such as communication systems, data storage and information security. However, the dimension and minimum distance of BCH codes are seldom solved until now because of their intractable characteristics. The objective of this paper is to study the dimensions of some BCH codes of length $n=2^m+1$ with $m=2t+1$, $4t+2$, $8t+4$ and $m\geq 10$. Some new techniques are employed to investigate coset leaders modulo $n$. For each type of $m$ above, the first five largest coset leaders modulo $n$ are determined, the dimension of some BCH codes of length $n$ with designed distance $δ>2^{\lceil \frac{m}{2} \rceil}$ is presented. These new techniques and results may be helpful to study other families of cyclic codes over finite fields.

cs.IT↗

arXiv2014

Formally self-dual linear binary codes from circulant graphs

In 2002, Tonchev first constructed some linear binary codes defined by the adjacency matrices of undirected graphs. So, graph is an important tool for searching optimum codes. In this paper, we introduce a new method of searching (proposed) optimum formally self-dual linear binary codes from circulant graphs.

math.CO↗

arXiv2014

Additive codes over $GF(4)$ from circulant graphs

In $2006$, Danielsen and Parker \cite{DP} proved that every self-dual additive code over $GF(4)$ is equivalent to a graph code. So, graph is an important tool for searching (proposed) optimum codes. In this paper, we introduce a new method of searching (proposed) optimum additive codes from circulant graphs.

math.CO↗

arXiv2009

On $[[n,n-4,3]]_{q}$ Quantum MDS Codes for odd prime power $q$

For each odd prime power $q$, let $4 \leq n\leq q^{2}+1$. Hermitian self-orthogonal $[n,2,n-1]$ codes over $GF(q^{2})$ with dual distance three are constructed by using finite field theory. Hence, $[[n,n-4,3]]_{q}$ quantum MDS codes for $4 \leq n\leq q^{2}+1$ are obtained.

cs.IT↗