MinT - Information on Result #664045

Information on Result #664045

Linear OA(9¹⁴⁰, 145, F₉, 114) (dual of [145, 5, 115]-code), using generalized (u,Â u+v)-construction based on

linear OA(9²⁵, 29, F₉, 22) (dual of [29, 4, 23]-code), using
- constructionÂ X applied to AG(F,4P) âŠ‚ AG(F,6P) [i] based on
  1. linear OA(9²⁴, 27, F₉, 22) (dual of [27, 3, 23]-code), using algebraic-geometric code AG(F,4P) with known gap numbers [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using the Hermitian function field over F₉ [i]
  2. linear OA(9²³, 27, F₉, 20) (dual of [27, 4, 21]-code), using algebraic-geometric code AG(F,6P) [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28 (see above)
  3. linear OA(9¹, 2, F₉, 1) (dual of [2, 1, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(9¹, s, F₉, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(9²⁸, 29, F₉, 28) (dual of [29, 1, 29]-code or 29-arc in PG(27,9)), using
- dual of repetition code with length 29 [i]
linear OA(9²⁹, 29, F₉, 29) (dual of [29, 0, 30]-code or 29-arc in PG(28,9)), using
- complete OA / dual of code with only one code word [i]
linear OA(9²⁹, 29, F₉, 29) (dual of [29, 0, 30]-code or 29-arc in PG(28,9)) (see above)
linear OA(9²⁹, 29, F₉, 29) (dual of [29, 0, 30]-code or 29-arc in PG(28,9)) (see above)

Mode: Constructive and linear.

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