MinT - Information on Result #911015

Information on Result #911015

Linear OOA(2¹¹², 60, F₂, 2, 64) (dual of [(60, 2), 8, 65]-NRT-code), using concatenation of two NRT-codes based on

linear OA(4¹⁶, 20, F₄, 12) (dual of [20, 4, 13]-code), using
- 3 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 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.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2¹¹², 60, F₂, 2, 63) (dual of [(60, 2), 8, 64]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹¹², 30, F₂, 4, 64) (dual of [(30, 4), 8, 65]-NRT-code)	[i]		OOA Folding