MinT - Information on Result #895788

Information on Result #895788

Linear OOA(4²⁴⁹, 4194391, F₄, 2, 25) (dual of [(4194391, 2), 8388533, 26]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4³², 90, F₄, 2, 12) (dual of [(90, 2), 148, 13]-NRT-code), using
- extracting embedded OOA [i] based on digital (20, 32, 90)-net over F₄, using
  - trace code for nets [i] based on digital (4, 16, 45)-net over F₁₆, using
    - net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
        a function field by GarcÃa and Quoos [i]
linear OOA(4²¹⁷, 4194301, F₄, 2, 25) (dual of [(4194301, 2), 8388385, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4²¹⁷, 8388602, F₄, 25) (dual of [8388602, 8388385, 26]-code), using
  - discarding factors / shortening the dual code based on linear OA(4²¹⁷, large, F₄, 25) (dual of [large, large−217, 26]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 4²⁴âˆ’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		This result only	Method
1	Linear OOA(4²⁴⁹, 4194391, F₄, 2, 24) (dual of [(4194391, 2), 8388533, 25]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(4²⁵⁰, 4194391, F₄, 2, 25) (dual of [(4194391, 2), 8388532, 26]-NRT-code)	[i]		OOA Duplication