MinT - Information on Result #662285

Information on Result #662285

Linear OA(4²⁶⁰, 262175, F₄, 35) (dual of [262175, 261915, 36]-code), using (u,Â u+v)-construction based on

linear OA(4²⁵, 30, F₄, 17) (dual of [30, 5, 18]-code), using
- (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
  1. linear OA(4⁶, 10, F₄, 5) (dual of [10, 4, 6]-code), using
    - discarding factors / shortening the dual code based on linear OA(4⁶, 12, F₄, 5) (dual of [12, 6, 6]-code), using
      - extended quadratic residue code Q_e(12,4) [i]
  2. linear OA(4⁹, 10, F₄, 8) (dual of [10, 1, 9]-code), using
    - strength reduction [i] based on linear OA(4⁹, 10, F₄, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,4)), using
      - dual of repetition code with length 10 [i]
  3. linear OA(4¹⁰, 10, F₄, 10) (dual of [10, 0, 11]-code or 10-arc in PG(9,4)), using
    - complete OA / dual of code with only one code word [i]
linear OA(4²³⁵, 262145, F₄, 35) (dual of [262145, 261910, 36]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145Â | 4¹⁸âˆ’1, defining interval IÂ =Â [0,17], and minimum distance dÂ â‰¥ |{−17,−16,…,17}|+1Â =Â 36 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(4²⁶⁰, 233046, F₄, 2, 35) (dual of [(233046, 2), 465832, 36]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(4²⁶⁰, 233046, F₄, 3, 35) (dual of [(233046, 3), 698878, 36]-NRT-code)	[i]
3	Digital (225, 260, 233046)-net over F₄	[i]