MinT - Information on Result #2419365

Information on Result #2419365

Linear OOA(2¹²⁴, 64, F₂, 2, 82) (dual of [(64, 2), 4, 83]-NRT-code), using strength reduction based on linear OOA(2¹²⁴, 64, F₂, 2, 83) (dual of [(64, 2), 4, 84]-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(2¹¹⁶, 60, F₂, 2, 79) (dual of [(60, 2), 4, 80]-NRT-code), using
  - concatenation of two NRT-codes [i] based on
    1. linear OA(4¹⁸, 20, F₄, 15) (dual of [20, 2, 16]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹⁸, 21, F₄, 15) (dual of [21, 3, 16]-code), using
        Simplex code S(3,4) [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(2¹²⁴, 32, F₂, 4, 82) (dual of [(32, 4), 4, 83]-NRT-code)	[i]		OOA Folding