Beacon · τ/31–47 Workbench

1) Preamble · prime length

Length Sequence Symbols

— Auto: 31→mseq, 47→Legendre Corr: —

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Autocorrelation shown as max sidelobe (periodic). ±1 symbols recommended for BPSK audio plants.

Version (v, 3 bits) Topology echo (1 bit) Template ID (6 bits)

Lane (2 bits)

Raw 12‑bit header (v|topo|tid|lane)

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Golay(24,12,8) codeword (23b Golay + even parity)

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We implement the standard (23,12,7) Golay by polynomial division, then append a single even parity bit to form (24,12,8).

Day (0–63, 6b) Cross‑cycle Δ (−32..31, 6b 2’s comp) Seed token (0–4095, 12b)

Anchor A (0–63, 6b) Anchor B (0–63, 6b) Flags (0–15, 4b)

Tuple (α, me/mp, Q, Gℏ/c³) mask (8b) Reserved (4b)

Descriptor bits (pre‑CRC)

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CRC‑16/CCITT (poly 0x1021), appended MSB→LSB

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Data symbols (5‑bit, padded to 19)

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Parity symbols (12)

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Codeword (31 symbols) · hex

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GF(32) uses primitive polynomial x⁵+x²+1 and generator roots α¹…α¹². Data shorter than 19 symbols is zero‑padded.

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Use pre‑ECC bits when testing symbolization; use post‑ECC when planting full frames in controlled channels.

Chip rate (chips/s) Repeat preamble Payload tail (silence ms)

Noise σ (16‑bit units) BPSK amplitude (|A|) Sample rate (Hz)

Download

We BPSK‑map ±1 symbols to {−A,+A}, embed under white noise σ, and export 16‑bit PCM WAV. Defaults plant at <5σ.