MinT - Information on Result #894439

Information on Result #894439

Linear OOA(2²³⁴, 4194341, F₂, 2, 18) (dual of [(4194341, 2), 8388448, 19]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²⁷, 40, F₂, 2, 9) (dual of [(40, 2), 53, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁹, 23, F₂, 2, 4) (dual of [(23, 2), 37, 5]-NRT-code), using
    - extracting embedded OOA [i] based on digital (5, 9, 23)-net over F₂, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(2¹⁸, 20, F₂, 2, 9) (dual of [(20, 2), 22, 10]-NRT-code), using
    - extracting embedded OOA [i] based on digital (9, 18, 20)-net over F₂, using
      - linear code embedding found in a computer search [i]
linear OOA(2²⁰⁷, 4194301, F₂, 2, 18) (dual of [(4194301, 2), 8388395, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2²⁰⁷, 8388602, F₂, 18) (dual of [8388602, 8388395, 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(2²³⁴, 2097170, F₂, 4, 18) (dual of [(2097170, 4), 8388446, 19]-NRT-code)	[i]		OOA Folding