MinT - Information on Result #941728

Information on Result #941728

Linear OOA(3¹⁰², 53, F₃, 2, 78) (dual of [(53, 2), 4, 79]-NRT-code), using juxtaposition based on

linear OOA(3⁶, 5, F₃, 2, 5) (dual of [(5, 2), 4, 6]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁶, 6, F₃, 2, 5) (dual of [(6, 2), 6, 6]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3⁶, 12, F₃, 5) (dual of [12, 6, 6]-code), using
    - extended Golay code G_e(3) [i]
linear OOA(3⁹², 48, F₃, 2, 72) (dual of [(48, 2), 4, 73]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(3⁴, 4, F₃, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;4,3) [i]
  2. linear OOA(3⁸⁴, 44, F₃, 2, 67) (dual of [(44, 2), 4, 68]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(3⁴, 4, F₃, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code) (see above)
      2. linear OOA(3⁷⁶, 40, F₃, 2, 62) (dual of [(40, 2), 4, 63]-NRT-code), using
        concatenation of two NRT-codes [i] based on
        linear OA(9⁸, 10, F₉, 8) (dual of [10, 2, 9]-code or 10-arc in PG(7,9)), using
        extended Reedâ€“Solomon code RS_e(2,9) [i]
        Simplex code S(2,9) [i]
        linear OOA(3⁶, 4, F₃, 2, 6) (dual of [(4, 2), 2, 7]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;2,3) [i]

Mode: Constructive and linear.

None.

The following results depend on this result: