MinT - Information on Result #1684532

Information on Result #1684532

Linear OOA(2¹⁹², 2066985, F₂, 7, 15) (dual of [(2066985, 7), 14468703, 16]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁹², 2066985, F₂, 4, 15) (dual of [(2066985, 4), 8267748, 16]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁹², 2097660, F₂, 4, 15) (dual of [(2097660, 4), 8390448, 16]-NRT-code), using
- 2¹ times duplication [i] based on linear OOA(2¹⁹¹, 2097660, F₂, 4, 15) (dual of [(2097660, 4), 8390449, 16]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2²⁹, 510, F₂, 4, 7) (dual of [(510, 4), 2011, 8]-NRT-code), using
      - OOA stacking with additional row [i] based on linear OOA(2²⁹, 511, F₂, 3, 7) (dual of [(511, 3), 1504, 8]-NRT-code), using
        OOAs constructed from BCH codes [i]
    2. linear OOA(2¹⁶², 2097150, F₂, 4, 15) (dual of [(2097150, 4), 8388438, 16]-NRT-code), using
      - OOA 4-folding [i] based on linear OA(2¹⁶², 8388600, F₂, 15) (dual of [8388600, 8388438, 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(2¹⁹², 2066984, F₂, 8, 15) (dual of [(2066984, 8), 16535680, 16]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹⁹², 2066984, F₂, 21, 15) (dual of [(2066984, 21), 43406472, 16]-NRT-code)	[i]		OOA Stacking with Additional Row