MinT - Information on Result #1653588

Information on Result #1653588

Linear OOA(2²³¹, 1677750, F₂, 5, 18) (dual of [(1677750, 5), 8388519, 19]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²⁴, 30, F₂, 5, 9) (dual of [(30, 5), 126, 10]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2²⁴, 30, F₂, 2, 9) (dual of [(30, 2), 36, 10]-NRT-code), using
  - 2¹ times duplication [i] based on linear OOA(2²³, 30, F₂, 2, 9) (dual of [(30, 2), 37, 10]-NRT-code), using
    - 1 times NRT-code embedding in larger space [i] based on linear OOA(2²¹, 29, F₂, 2, 9) (dual of [(29, 2), 37, 10]-NRT-code), using
      - extracting embedded OOA [i] based on digital (12, 21, 29)-net over F₂, using
        linear code embedding found in a computer search [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(2²³¹, 1677750, F₂, 6, 18) (dual of [(1677750, 6), 10066269, 19]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²³¹, 1677750, F₂, 7, 18) (dual of [(1677750, 7), 11744019, 19]-NRT-code)	[i]
3	Linear OOA(2²³¹, 1677750, F₂, 8, 18) (dual of [(1677750, 8), 13421769, 19]-NRT-code)	[i]
4	Digital (213, 231, 1677750)-net over F₂	[i]