MinT - Information on Result #895791

Information on Result #895791

Linear OOA(4²⁵⁶, 4194541, F₄, 2, 25) (dual of [(4194541, 2), 8388826, 26]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4³⁹, 240, F₄, 2, 12) (dual of [(240, 2), 441, 13]-NRT-code), using
- extracting embedded OOA [i] based on digital (27, 39, 240)-net over F₄, using
  - trace code for nets [i] based on digital (1, 13, 80)-net over F₆₄, using
    - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
        a function field by SÃ©mirat [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		Method
1	Linear OOA(4²⁵⁶, 4194541, F₄, 2, 24) (dual of [(4194541, 2), 8388826, 25]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(4²⁵⁸, 4194542, F₄, 2, 25) (dual of [(4194542, 2), 8388826, 26]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(4²⁶⁰, 4194543, F₄, 2, 25) (dual of [(4194543, 2), 8388826, 26]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
4	Linear OOA(4²⁵⁷, 4194541, F₄, 2, 25) (dual of [(4194541, 2), 8388825, 26]-NRT-code)	[i]	OOA Duplication