bb288

Description

A bivariate bicycle (BB) code with parameters [[288,12,18]] and weight-six stabilizer generators \cite{arxiv:2308.07915}. One defining presentation uses \((\ell,m)=(12,12)\) with x^{\ell}=y^{m}=1, and A=x^3+y^2+y^7, \(B=y^3+x+x^…

Introduced in: arxiv:2308.07915

Rationale

Re-scored 2026-07-18: IBM's double-gross [[288,12,18]], the roadmap successor to the now-formalized gross code. Moonshot proper: A14 refuted the safe-floor/doubling route on BOTH axes of the stored presentation (x: raw seam weight 24; y: weight-34 witness beyond the cheap tiers), and A17's deficit-wall theorem constrains what the safe sector can deliver — so d = 18 needs genuinely new mathematics (presentation-orbit rescue, mixed 'tour-de-gross' lifts, or a new floor mechanism; all open per A14/A17). The A16 class theorem would give only d >= 6. All BB chain-complex/cover infrastructure applies (reuse 9); the missing piece is the distance mechanism itself. Previous rationale: Re-scored 2026-05-23: `QEC/Stabilizer/Homological/BBChainComplex.lean` (~285 LoC, on main from the gross moonshot Approach A) now provides the generic BB chain complex framework for any finite abelian G + polynomial pair (A,B) in F_2[G], plus convolution algebra and the abstract `chainWeight_lower_bound_transfers` distance-bridge combinator. Prerequisites bumped from 4 -> 6 (partial unblock). Distance-bound machinery (tight algebraic / homological argument) is still open per the gross Approach A + B negative results, so tractability remains low.

Blockers: new distance mechanism — safe-floor/doubling SF-refuted on both axes (A14); presentation orbits / mixed lifts open (A17)

Scoring composite 6.15