MinT - Information on Result #1590108

Information on Result #1590108

Linear OOA(2¹⁰⁴, 3604519, F₂, 4, 8) (dual of [(3604519, 4), 14417972, 9]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁰⁴, 3604519, F₂, 2, 8) (dual of [(3604519, 2), 7208934, 9]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁰⁴, 4194366, F₂, 2, 8) (dual of [(4194366, 2), 8388628, 9]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹², 65, F₂, 2, 4) (dual of [(65, 2), 118, 5]-NRT-code), using
    - extracting embedded OOA [i] based on digital (8, 12, 65)-net over F₂, using
      - nets constructed from net-embeddable BCH codes [i]
  2. linear OOA(2⁹², 4194301, F₂, 2, 8) (dual of [(4194301, 2), 8388510, 9]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2⁹², 8388602, F₂, 8) (dual of [8388602, 8388510, 9]-code), using
      - discarding factors / shortening the dual code based on linear OA(2⁹², large, F₂, 8) (dual of [large, large−92, 9]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]

Mode: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2¹⁰⁴, 3604518, F₂, 5, 8) (dual of [(3604518, 5), 18022486, 9]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹⁰⁴, 3604518, F₂, 6, 8) (dual of [(3604518, 6), 21627004, 9]-NRT-code)	[i]
3	Linear OOA(2¹⁰⁴, 3604518, F₂, 7, 8) (dual of [(3604518, 7), 25231522, 9]-NRT-code)	[i]
4	Linear OOA(2¹⁰⁴, 3604518, F₂, 8, 8) (dual of [(3604518, 8), 28836040, 9]-NRT-code)	[i]