MinT - Information on Result #640848

Information on Result #640848

Linear OA(2¹⁷⁰, 178, F₂, 86) (dual of [178, 8, 87]-code), using juxtaposition based on

linear OA(2⁴², 50, F₂, 22) (dual of [50, 8, 23]-code), using
- 1 times truncation [i] based on linear OA(2⁴³, 51, F₂, 23) (dual of [51, 8, 24]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(4¹³, 17, F₄, 11) (dual of [17, 4, 12]-code), using
      - projective code from ovoid in PG(3,Â 4) [i]
    2. linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
linear OA(2¹²⁰, 128, F₂, 63) (dual of [128, 8, 64]-code), using
- Reedâ€“Muller code RM(5,7) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(2¹⁷¹, 179, F₂, 87) (dual of [179, 8, 88]-code)	[i]		Adding a Parity Check Bit
2	Linear OOA(2¹⁷⁰, 89, F₂, 2, 86) (dual of [(89, 2), 8, 87]-NRT-code)	[i]		OOA Folding