相关论文: Quantum Weight Enumerators

In a recent paper [quant-ph/9610040], Shor and Laflamme define two ``weight enumerators'' for quantum error correcting codes, connected by a MacWilliams transform, and use them to give a linear-programming bound for quantum codes. We extend…

In 1997, Shor and Laflamme defined the weight enumerators for quantum error-correcting codes and derived a MacWilliams identity. We extend their work by introducing our double weight enumerators and complete weight enumerators. The…

While quantum weight enumerators establish some of the best upper bounds on the minimum distance of quantum error-correcting codes, these bounds are not optimized to quantify the performance of quantum codes under the effect of arbitrary…

Quantum weight enumerators are fundamental tools for analyzing quantum error-correcting codes and multipartite entanglement, offering insights into the existence of quantum error-correcting codes and $k$-uniform states. In this work, we…

This article is a continuation of our recent work (Yin Chen and Runxuan Zhang, Shape enumerators of self-dual NRT codes over finite fields. SIAM J. Discrete Math. 38 (2024), no. 4, 2841-2854) in the setting of quantum error-correcting…

In this note we show that the weight enumerators of a real quantum error correcting code with $ X $ and $ Z $ exactly transversal must satisfy certain identities. One consequence of these identities is that if the code is error detecting…

We provide the first tensor network method for computing quantum weight enumerator polynomials in the most general form. If a quantum code has a known tensor network construction of its encoding map, our method is far more efficient, and in…

We examine the use of weight enumerators for analyzing tensor network constructions, and specifically the quantum lego framework recently introduced. We extend the notion of quantum weight enumerators to so-called tensor enumerators, and…

Given that approximate quantum error-correcting (AQEC) codes have a potentially better performance than perfect quantum error correction codes, it is pertinent to quantify their performance. While quantum weight enumerators establish some…

We show that one of the Shor-Laflamme weight enumerators of a codeword stabilized quantum code may be interpreted as the distance enumerator of an associated classical code.

Linear programming approaches have been applied to derive upper bounds on the size of classical codes and quantum codes. In this paper, we derive similar results for general quantum codes with entanglement assistance, including nonadditive…

Let $\mathbb{F}_q$ be a finite field of characteristic not equal to $2$ or $3$. We compute the weight enumerators of some projective and affine Reed-Muller codes of order $3$ over $\mathbb{F}_q$. These weight enumerators answer enumerative…

In this paper we present a new method for finding the weight enumerator of binary linear block codes by using genetic algorithms. This method consists in finding the binary weight enumerator of the code and its dual and to create from the…

Throughout its history, the theory of quantum error correction has heavily benefited from translating classical concepts into the quantum setting. In particular, classical notions of weight enumerators, which relate to the performance of an…

In the 1960s, MacWilliams proved that the Hamming weight enumerator of a linear code over a finite field completely determines, and is determined by, the Hamming weight enumerator of its dual code. In particular, if two linear codes have…

In this paper, we consider codes over finite fields, finite abelian groups, and finite Frobenius rings. For such codes, the complete weight enumerator and the Hamming weight enumerator serve as powerful tools. These two types of weight…

The weight enumerators (quant-ph/9610040) of a quantum code are quite powerful tools for exploring its structure. As the weight enumerators are quadratic invariants of the code, this suggests the consideration of higher-degree polynomial…

We develop an intrinsic enumerator framework for quantum error correction in unitary representations of symmetry groups. An intrinsic quantum code is a subspace of a representation $V$ of a group $G$, and errors are organized by the…

Quantum weight reduction is the task of transforming a quantum code with large check weight into one with small check weight. Low-weight codes are essential for implementing quantum error correction on physical hardware, since high-weight…

Weight enumerators are important tools for deciphering the algebraic structure of the related code spaces and for understanding group actions on these spaces. Our study focuses on symmetrized weight enumerators of pairs of Type II codes…