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Pin-Chieh Tseng

Publications and source records attributed to Pin-Chieh Tseng.

5 recordsLinked to original sources
arXiv2024

Semidefinite programming bounds on the size of entanglement-assisted codeword stabilized quantum codes

In this paper, we explore the application of semidefinite programming to the realm of quantum codes, specifically focusing on codeword stabilized (CWS) codes with entanglement assistance. Notably, we utilize the isotropic subgroup of the CWS group and the set of word operators of a CWS-type quantum code to derive an upper bound on the minimum distance. Furthermore, this characterization can be incorporated into the associated distance enumerators, enabling us to construct semidefinite constraints that lead to SDP bounds on the minimum distance or size of CWS-type quantum codes. We illustrate several instances where SDP bounds outperform LP bounds, and there are even cases where LP fails to yield meaningful results, while SDP consistently provides tighter and relevant bounds. Finally, we also provide interpretations of the Shor-Laflamme weight enumerators and shadow enumerators for codeword stabilized codes, enhancing our understanding of quantum codes.

quant-ph↗
arXiv2023

Semidefinite programming bounds for binary codes from a split Terwilliger algebra

We study the upper bounds for $A(n,d)$, the maximum size of codewords with length $n$ and Hamming distance at least $d$. Schrijver studied the Terwilliger algebra of the Hamming scheme and proposed a semidefinite program to bound $A(n, d)$. We derive more sophisticated matrix inequalities based on a split Terwilliger algebra to improve Schrijver's semidefinite programming bounds on $A(n, d)$. In particular, we improve the semidefinite programming bounds on $A(18,4)$ to $6551$.

cs.IT↗
arXiv2023

An Error-Correction Model for Information Transmissions of Social Networks

We study the error-correction problem of the communication between two vertices in a social network. By applying the concepts of coding theory into the Social Network Analysis (SNA), we develop the code social network model, which can offer an efficient way to ensure the correctness of the message transmission within the social netwoks. The result of this study could apply in vary of social science studies.

cs.SI↗
arXiv2022

On the size of maximal binary codes with 2, 3, and 4 distances

We address the maximum size of binary codes and binary constant weight codes with few distances. Previous works established a number of bounds for these quantities as well as the exact values for a range of small code lengths. As our main results, we determine the exact size of maximal binary codes with two distances for all lengths $n\ge 6$ as well as the exact size of maximal binary constant weight codes with 2,3, and 4 distances for several values of the weight and for all but small lengths.

math.CO↗