MinT - Information on Result #1516354

Information on Result #1516354

Linear OOA(2²¹⁵, 3311673, F₂, 3, 14) (dual of [(3311673, 3), 9934804, 15]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²¹⁵, 3311673, F₂, 2, 14) (dual of [(3311673, 2), 6623131, 15]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²¹⁵, 4325372, F₂, 2, 14) (dual of [(4325372, 2), 8650529, 15]-NRT-code), using
- strength reduction [i] based on linear OOA(2²¹⁵, 4325372, F₂, 2, 15) (dual of [(4325372, 2), 8650529, 16]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2⁵³, 131071, F₂, 2, 7) (dual of [(131071, 2), 262089, 8]-NRT-code), using
      - extracting embedded OOA [i] based on digital (46, 53, 131071)-net over F₂, using
        nets constructed from net-embeddable BCH codes [i]
    2. linear OOA(2¹⁶², 4194301, F₂, 2, 15) (dual of [(4194301, 2), 8388440, 16]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(2¹⁶², 8388602, F₂, 15) (dual of [8388602, 8388440, 16]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹⁶², large, F₂, 15) (dual of [large, large−162, 16]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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(2²¹⁵, 1655836, F₂, 6, 14) (dual of [(1655836, 6), 9934801, 15]-NRT-code)	[i]		OOA Folding