MinT - Information on Result #1027344

Information on Result #1027344

Linear OOA(4²⁵², 86, F₄, 3, 206) (dual of [(86, 3), 6, 207]-NRT-code), using juxtaposition based on

linear OOA(4¹², 6, F₄, 3, 11) (dual of [(6, 3), 6, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4¹², 9, F₄, 3, 11) (dual of [(9, 3), 15, 12]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,15P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
    - the Hermitian function field over F₄ [i]
linear OOA(4²³⁴, 80, F₄, 3, 194) (dual of [(80, 3), 6, 195]-NRT-code), using
- strength reduction [i] based on linear OOA(4²³⁴, 80, F₄, 3, 195) (dual of [(80, 3), 6, 196]-NRT-code), using
  - concatenation of two NRT-codes [i] based on
    1. linear OA(16¹³, 16, F₁₆, 13) (dual of [16, 3, 14]-code or 16-arc in PG(12,16)), using
      - Reedâ€“Solomon code RS(3,16) [i]
    2. linear OOA(4¹³, 5, F₄, 3, 13) (dual of [(5, 3), 2, 14]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(3;2,4) [i]

Mode: Constructive and linear.

None.

The following results depend on this result: