We construct nested Calderbank-Shor-Steane code pairs with non-vanishing coding rate from Hsu-Anastasopoulos codes and MacKay-Neal codes. In the fixed-degree regime, we prove relative linear distance with high probability. Moreover, for several finite degree settings, we prove Gilbert-Varshamov distance by a rigorous computer-assisted proof.

翻译：我们利用Hsu-Anastasopoulos码和MacKay-Neal码构造了具有非零码率的嵌套Calderbank-Shor-Steane码对。在固定度情形下，我们以高概率证明了相对线性距离。此外，对于若干有限度设置，我们通过严格的计算机辅助证明确立了Gilbert-Varshamov距离。