MinT - Information on Result #1653593

Information on Result #1653593

Linear OOA(2²³⁹, 1677806, F₂, 5, 18) (dual of [(1677806, 5), 8388791, 19]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2³², 86, F₂, 5, 9) (dual of [(86, 5), 398, 10]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2³², 86, F₂, 2, 9) (dual of [(86, 2), 140, 10]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2³², 172, F₂, 9) (dual of [172, 140, 10]-code), using
    - adding a parity check bit [i] based on linear OA(2³¹, 171, F₂, 8) (dual of [171, 140, 9]-code), using
      - a â€œGraâ€ code from Grasslâ€™s database [i]
linear OOA(2²⁰⁷, 1677720, F₂, 5, 18) (dual of [(1677720, 5), 8388393, 19]-NRT-code), using
- OOA 5-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: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²³⁹, 1677806, F₂, 6, 18) (dual of [(1677806, 6), 10066597, 19]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²³⁹, 1677806, F₂, 7, 18) (dual of [(1677806, 7), 11744403, 19]-NRT-code)	[i]
3	Linear OOA(2²³⁹, 1677806, F₂, 8, 18) (dual of [(1677806, 8), 13422209, 19]-NRT-code)	[i]
4	Digital (221, 239, 1677806)-net over F₂	[i]