MinT - Information on Result #1440179

Information on Result #1440179

Linear OOA(5¹⁴³, 331909, F₅, 2, 21) (dual of [(331909, 2), 663675, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(5¹⁴³, 331909, F₅, 21) (dual of [331909, 331766, 22]-code), using

discarding factors / shortening the dual code based on linear OA(5¹⁴³, 390655, F₅, 21) (dual of [390655, 390512, 22]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(5¹⁴, 29, F₅, 10) (dual of [29, 15, 11]-code), using
    - 1 times truncation [i] based on linear OA(5¹⁵, 30, F₅, 11) (dual of [30, 15, 12]-code), using
      - extended quadratic residue code Q_e(30,5) [i]
  2. linear OA(5¹²⁹, 390626, F₅, 21) (dual of [390626, 390497, 22]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 390626Â | 5¹⁶âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(5¹⁴³, 165954, F₅, 3, 21) (dual of [(165954, 3), 497719, 22]-NRT-code)	[i]		OOA Folding