MinT - Information on Result #2420897

Information on Result #2420897

Linear OOA(2¹⁵², 78, F₂, 2, 100) (dual of [(78, 2), 4, 101]-NRT-code), using strength reduction based on linear OOA(2¹⁵², 78, F₂, 2, 101) (dual of [(78, 2), 4, 102]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2⁴, 4, F₂, 2, 3) (dual of [(4, 2), 4, 4]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(2⁴, 7, F₂, 2, 3) (dual of [(7, 2), 10, 4]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OA(2⁴, 8, F₂, 3) (dual of [8, 4, 4]-code or 8-cap in PG(3,2)), using
      - Reedâ€“Muller code RM(1,3) [i]
      - caps in base bÂ =Â 2 [i]
2. linear OOA(2¹⁴⁴, 74, F₂, 2, 97) (dual of [(74, 2), 4, 98]-NRT-code), using
  - 2 step truncation [i] based on linear OOA(2¹⁴⁶, 75, F₂, 2, 99) (dual of [(75, 2), 4, 100]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OA(4²³, 25, F₄, 19) (dual of [25, 2, 20]-code), using
        repeating each code word 5 times [i] based on linear OA(4³, 5, F₄, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,4) or 5-cap in PG(2,4)), using
        extended Reedâ€“Solomon code RS_e(2,4) [i]
        Simplex code S(2,4) [i]
      2. linear OOA(2⁴, 3, F₂, 2, 4) (dual of [(3, 2), 2, 5]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;2,2) [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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2¹⁵², 39, F₂, 4, 100) (dual of [(39, 4), 4, 101]-NRT-code)	[i]		OOA Folding