MinT - Information on Result #669647

Information on Result #669647

Linear OA(64⁵⁶, 210, F₆₄, 33) (dual of [210, 154, 34]-code), using (u,Â u+v)-construction based on

linear OA(64¹⁹, 104, F₆₄, 16) (dual of [104, 85, 17]-code), using
- extended algebraic-geometric code AG_e(F,87P) [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
  - a function field by SÃ©mirat [i]
linear OA(64³⁷, 106, F₆₄, 33) (dual of [106, 69, 34]-code), using
- constructionÂ X applied to AG(F,69P) âŠ‚ AG(F,71P) [i] based on
  1. linear OA(64³⁶, 103, F₆₄, 33) (dual of [103, 67, 34]-code), using algebraic-geometric code AG(F,69P) [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104 (see above)
  2. linear OA(64³⁴, 103, F₆₄, 31) (dual of [103, 69, 32]-code), using algebraic-geometric code AG(F,71P) [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104 (see above)
  3. linear OA(64¹, 3, F₆₄, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]

Mode: Constructive and linear.

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