Binary CSS-T codes: characterizations and posets

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" summary

Gives an equivalent, actionable characterization of binary CSS-T pairs: a pair C1 ⊇ C2 is CSS-T exactly when C2 ⊆ C1 ∩ (C2^2)⊥, replacing the original self-dual-on-support condition. Uses the star product/square of codes, hulls, shortening/puncturing and a partial order on pairs to propagate and maximize codes. Proves a propagation lemma that adds one vector to C1 (preserving distance if non‑degenerate) and produces new Reed‑Muller and cyclic/extended‑cyclic examples with improved parameters and explicit tables.

AI-written summary · about

" chapters (8)

1. 0:00Introduction
2. 1:03CSS-T codes over F2
3. 8:35Equivalent conditions
4. 13:41Poset structure
5. 17:40Reed-Muller as CSS-T
6. 19:28Cyclic codes construction
7. 22:45New examples and parameters
8. 23:07Q&A

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