PUZZLE #5589: FHSS Frequency Hopping (diff 5)

fhss learn difficulty: 5/7 simulate author: system unsolved

6 characters transmitted over 28 channels (14 jammed). Each character sent 3 times. LCG seed 5910 governs the hop schedule.

DATA

Hop Frequencies	`15, 4, 25, 6, 19, 12, 25, 10, 11, 12, 13, 22, 23, 20, 13, 6, 7, 20`
Transmissions	{'hop': 0, 'freq': 15, 'char_idx': 0, 'char': 'J', 'jammed': False}, {'hop': 1, 'freq': 4, 'char_idx': 1, 'char': 'U', 'jammed': False}, {'hop': 2, 'freq': 25, 'char_idx': 2, 'char': None, 'jammed': True}, {'hop': 3, 'freq': 6, 'char_idx': 3, 'char': None, 'jammed': True}, {'hop': 4, 'freq': 19, 'char_idx': 4, 'char': 'Q', 'jammed': False}, {'hop': 5, 'freq': 12, 'char_idx': 5, 'char': 'Y', 'jammed': False}, {'hop': 6, 'freq': 25, 'char_idx': 0, 'char': None, 'jammed': True}, {'hop': 7, 'freq': 10, 'char_idx': 1, 'char': None, 'jammed': True}, {'hop': 8, 'freq': 11, 'char_idx': 2, 'char': None, 'jammed': True}, {'hop': 9, 'freq': 12, 'char_idx': 3, 'char': 'B', 'jammed': False}, {'hop': 10, 'freq': 13, 'char_idx': 4, 'char': 'Q', 'jammed': False}, {'hop': 11, 'freq': 22, 'char_idx': 5, 'char': 'Y', 'jammed': False}, {'hop': 12, 'freq': 23, 'char_idx': 0, 'char': 'J', 'jammed': False}, {'hop': 13, 'freq': 20, 'char_idx': 1, 'char': None, 'jammed': True}, {'hop': 14, 'freq': 13, 'char_idx': 2, 'char': 'G', 'jammed': False}, {'hop': 15, 'freq': 6, 'char_idx': 3, 'char': None, 'jammed': True}, {'hop': 16, 'freq': 7, 'char_idx': 4, 'char': 'Q', 'jammed': False}, {'hop': 17, 'freq': 20, 'char_idx': 5, 'char': None, 'jammed': True}
Jammed Channels	`0, 3, 5, 6, 8, 10, 11, 14, 16, 18, 20, 21, 24, 25`
N Channels	`28`
N Chars	`6`
Redundancy	`3`
Seed	`5910`
Lcg A	`1103515245`
Lcg C	`12345`
Lcg M	`2147483648`
Hint	`LCG: x_i+1 = (a·x_i + c) mod m. Compute hop sequence from seed, find which hops survived jamming. Group surviving letters by char_idx to reconstruct the word.`
Answer Format	`lowercase word, no spaces or punctuation`

{
  "type": "fhss",
  "hop_frequencies": [
    15,
    4,
    25,
    6,
    19,
    12,
    25,
    10,
    11,
    12,
    13,
    22,
    23,
    20,
    13,
    6,
    7,
    20
  ],
  "transmissions": [
    {
      "hop": 0,
      "freq": 15,
      "char_idx": 0,
      "char": "J",
      "jammed": false
    },
    {
      "hop": 1,
      "freq": 4,
      "char_idx": 1,
      "char": "U",
      "jammed": false
    },
    {
      "hop": 2,
      "freq": 25,
      "char_idx": 2,
      "char": null,
      "jammed": true
    },
    {
      "hop": 3,
      "freq": 6,
      "char_idx": 3,
      "char": null,
      "jammed": true
    },
    {
      "hop": 4,
      "freq": 19,
      "char_idx": 4,
      "char": "Q",
      "jammed": false
    },
    {
      "hop": 5,
      "freq": 12,
      "char_idx": 5,
      "char": "Y",
      "jammed": false
    },
    {
      "hop": 6,
      "freq": 25,
      "char_idx": 0,
      "char": null,
      "jammed": true
    },
    {
      "hop": 7,
      "freq": 10,
      "char_idx": 1,
      "char": null,
      "jammed": true
    },
    {
      "hop": 8,
      "freq": 11,
      "char_idx": 2,
      "char": null,
      "jammed": true
    },
    {
      "hop": 9,
      "freq": 12,
      "char_idx": 3,
      "char": "B",
      "jammed": false
    },
    {
      "hop": 10,
      "freq": 13,
      "char_idx": 4,
      "char": "Q",
      "jammed": false
    },
    {
      "hop": 11,
      "freq": 22,
      "char_idx": 5,
      "char": "Y",
      "jammed": false
    },
    {
      "hop": 12,
      "freq": 23,
      "char_idx": 0,
      "char": "J",
      "jammed": false
    },
    {
      "hop": 13,
      "freq": 20,
      "char_idx": 1,
      "char": null,
      "jammed": true
    },
    {
      "hop": 14,
      "freq": 13,
      "char_idx": 2,
      "char": "G",
      "jammed": false
    },
    {
      "hop": 15,
      "freq": 6,
      "char_idx": 3,
      "char": null,
      "jammed": true
    },
    {
      "hop": 16,
      "freq": 7,
      "char_idx": 4,
      "char": "Q",
      "jammed": false
    },
    {
      "hop": 17,
      "freq": 20,
      "char_idx": 5,
      "char": null,
      "jammed": true
    }
  ],
  "jammed_channels": [
    0,
    3,
    5,
    6,
    8,
    10,
    11,
    14,
    16,
    18,
    20,
    21,
    24,
    25
  ],
  "n_channels": 28,
  "n_chars": 6,
  "redundancy": 3,
  "seed": 5910,
  "lcg_a": 1103515245,
  "lcg_c": 12345,
  "lcg_m": 2147483648,
  "hint": "LCG: x_i+1 = (a\u00b7x_i + c) mod m. Compute hop sequence from seed, find which hops survived jamming. Group surviving letters by char_idx to reconstruct the word.",
  "answer_format": "lowercase word, no spaces or punctuation"
}

author's note: Pool fill: fhss diff 5