MinT - Information on Result #1599090

Information on Result #1599090

Linear OOA(2²⁴², 1369, F₂, 4, 40) (dual of [(1369, 4), 5234, 41]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁴², 1369, F₂, 3, 40) (dual of [(1369, 3), 3865, 41]-NRT-code), using

strength reduction [i] based on linear OOA(2²⁴², 1369, F₂, 3, 41) (dual of [(1369, 3), 3865, 42]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2²⁴², 4107, F₂, 41) (dual of [4107, 3865, 42]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²⁴², 4109, F₂, 41) (dual of [4109, 3867, 42]-code), using
    - constructionÂ X applied to C_e(40) âŠ‚ C_e(38) [i] based on
      1. linear OA(2²⁴¹, 4096, F₂, 41) (dual of [4096, 3855, 42]-code), using an extension C_e(40) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,40], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 41 [i]
      2. linear OA(2²²⁹, 4096, F₂, 39) (dual of [4096, 3867, 40]-code), using an extension C_e(38) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,38], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [i]
      3. linear OA(2¹, 13, F₂, 1) (dual of [13, 12, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n 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(2²⁴², 684, F₂, 7, 40) (dual of [(684, 7), 4546, 41]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²⁴², 684, F₂, 8, 40) (dual of [(684, 8), 5230, 41]-NRT-code)	[i]		OOA Folding