MinT - Information on Result #895784

Information on Result #895784

Linear OOA(4²⁴¹, 4194335, F₄, 2, 25) (dual of [(4194335, 2), 8388429, 26]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4²⁴, 34, F₄, 2, 12) (dual of [(34, 2), 44, 13]-NRT-code), using
- extracting embedded OOA [i] based on digital (12, 24, 34)-net over F₄, using
  - trace code for nets [i] based on digital (0, 12, 17)-net over F₁₆, using
    - net from sequence [i] based on digital (0, 16)-sequence over F₁₆, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 0 and N(F) ≥ 17, using
        the rational function field F₁₆(x) [i]
      - Niederreiter sequence [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(4²⁴¹, 4194335, F₄, 2, 24) (dual of [(4194335, 2), 8388429, 25]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(4²⁴², 4194335, F₄, 2, 25) (dual of [(4194335, 2), 8388428, 26]-NRT-code)	[i]		OOA Duplication