MinT - Information on Result #662424

Information on Result #662424

Linear OA(4¹⁷⁹, 262165, F₄, 25) (dual of [262165, 261986, 26]-code), using (u,Â u+v)-construction 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 OA(4¹⁶³, 262145, F₄, 25) (dual of [262145, 261982, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145Â | 4¹⁸âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(4¹⁷⁹, 143450, F₄, 2, 25) (dual of [(143450, 2), 286721, 26]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(4¹⁷⁹, 143450, F₄, 3, 25) (dual of [(143450, 3), 430171, 26]-NRT-code)	[i]
3	Digital (154, 179, 143450)-net over F₄	[i]