MinT - Information on Result #661422

Information on Result #661422

Linear OA(2⁵⁸, 66, F₂, 29) (dual of [66, 8, 30]-code), using concatenation of two codes based on

linear OA(4¹⁸, 22, F₄, 14) (dual of [22, 4, 15]-code), using
- 1 times truncation [i] based on linear OA(4¹⁹, 23, F₄, 15) (dual of [23, 4, 16]-code), using
  - constructionÂ X applied to C₁ âŠ‚ C₂ with C₁ a [17,1,16]-code [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(4³, 6, F₄, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,4) or 6-cap in PG(2,4)), using
      - hyperoval in PG(2,Â 4) [i]
      - the Hexacode [i]
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]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2⁵⁸, 22, F₂, 3, 29) (dual of [(22, 3), 8, 30]-NRT-code)	[i]		OOA Folding