MinT - Information on Result #2431105

Information on Result #2431105

Linear OOA(3¹⁰², 53, F₃, 2, 77) (dual of [(53, 2), 4, 78]-NRT-code), using strength reduction based on linear OOA(3¹⁰², 53, F₃, 2, 78) (dual of [(53, 2), 4, 79]-NRT-code), using

juxtaposition [i] based on
1. 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]
2. 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
        linear OOA(3⁴, 4, F₃, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code) (see above)
        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.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.