Abstract: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 codes. We use algebraic invariant theory to study three weight enumerators of formally self-dual quantum codes over arbitrary finite fields. We derive a quantum analogue of Gleason's theorem, demonstrating that the weight enumerator of a formally self-dual quantum code can be expressed algebraically by two polynomials. We also show that the double weight enumerator of a formally self-dual quantum code can be expressed algebraically by five polynomials. We explicitly compute the complete weight enumerators of some special self-dual quantum codes. Our approach illustrates the potential of employing algebraic invariant theory to compute weight enumerators of self-dual quantum codes.
From: Yin Chen [view email]
[v1]
Thu, 5 Sep 2024 14:30:58 UTC (16 KB)
[v2]
Fri, 15 Nov 2024 17:28:04 UTC (16 KB)
[v3]
Tue, 27 Jan 2026 01:49:54 UTC (20 KB)
[v4]
Sat, 27 Jun 2026 14:59:28 UTC (20 KB)
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