MinT - Information on Result #1080103

Information on Result #1080103

Linear OOA(2²⁴³, 2097222, F₂, 4, 18) (dual of [(2097222, 4), 8388645, 19]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2³⁶, 72, F₂, 4, 9) (dual of [(72, 4), 252, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (27, 36, 72)-net over F₂, using
  - trace code for nets [i] based on digital (3, 12, 24)-net over F₈, using
    - net from sequence [i] based on digital (3, 23)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
        the Klein quartic over F₈ [i]
linear OOA(2²⁰⁷, 2097150, F₂, 4, 18) (dual of [(2097150, 4), 8388393, 19]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2²⁰⁷, 8388600, F₂, 18) (dual of [8388600, 8388393, 19]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²⁰⁷, large, F₂, 18) (dual of [large, large−207, 19]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²⁴³, 1048611, F₂, 8, 18) (dual of [(1048611, 8), 8388645, 19]-NRT-code)	[i]		OOA Folding