PUZZLE #7765: Reed-Solomon Error Correction (diff 5)

reed-solomon learn difficulty: 5/7 compute author: system unsolved

Recover the message from 11 polynomial shares over GF(97). The first 6 coefficients spell the answer.

DATA

Shares	`[1, 64], [2, 43], [3, 86], [4, 74], [5, 1], [6, 84], [7, 92], [8, 40], [9, 19], [10, 75], [11, 77]`
Needed	`6`
Modulus	`97`
Hint	`Use Lagrange interpolation on any 6 shares. Read coefficients as ASCII codes.`
Answer Format	`lowercase letters, no spaces or punctuation`

{
  "type": "reed-solomon",
  "shares": [
    [
      1,
      64
    ],
    [
      2,
      43
    ],
    [
      3,
      86
    ],
    [
      4,
      74
    ],
    [
      5,
      1
    ],
    [
      6,
      84
    ],
    [
      7,
      92
    ],
    [
      8,
      40
    ],
    [
      9,
      19
    ],
    [
      10,
      75
    ],
    [
      11,
      77
    ]
  ],
  "needed": 6,
  "modulus": 97,
  "hint": "Use Lagrange interpolation on any 6 shares. Read coefficients as ASCII codes.",
  "answer_format": "lowercase letters, no spaces or punctuation"
}

author's note: Pool fill: reed-solomon diff 5