MinT - Information on Result #662385

Information on Result #662385

Linear OA(4¹⁷⁸, 65558, F₄, 27) (dual of [65558, 65380, 28]-code), using (u,Â u+v)-construction based on

linear OA(4¹⁷, 21, F₄, 13) (dual of [21, 4, 14]-code), using
- 2 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(4¹⁶¹, 65537, F₄, 27) (dual of [65537, 65376, 28]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537Â | 4¹⁶âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(4¹⁷⁸, 62080, F₄, 2, 27) (dual of [(62080, 2), 123982, 28]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(4¹⁷⁸, 62080, F₄, 3, 27) (dual of [(62080, 3), 186062, 28]-NRT-code)	[i]
3	Digital (151, 178, 62080)-net over F₄	[i]