Weight enumerators of self-dual quantum codes
<|reference_start|>Weight enumerators of self-dual quantum codes: We use algebraic invariant theory to study three weight enumerators of self-dual quantum codes over finite fields. We show that the weight enumerators of self-dual quantum codes can be expressed algebraically by two polynomials and the double weight enumerators of self-dual quantum codes can be expressed algebraically by five polynomials. We also explicitly compute the complete weight enumerators of some special self-dual quantum codes. Our approach avoids applying the well-known Molien's formula and demonstrates the potential of employing invariant theory to compute weight enumerators of quantum codes.<|reference_end|>
@article{chen2024weight,
    title={Weight enumerators of self-dual quantum codes},
    author={Yin Chen and Shan Ren},
    journal={arXiv preprint arXiv:2409.03576},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.03576},
    primaryClass={cs.IT math.IT}
}