MinT - Information on Result #1698332

Information on Result #1698332

Linear OOA(2¹³⁴, 1048582, F₂, 8, 12) (dual of [(1048582, 8), 8388522, 13]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹³⁴, 1048582, F₂, 4, 12) (dual of [(1048582, 4), 4194194, 13]-NRT-code), using

OOA 4-folding [i] based on linear OA(2¹³⁴, 4194328, F₂, 12) (dual of [4194328, 4194194, 13]-code), using
- strength reduction [i] based on linear OA(2¹³⁴, 4194328, F₂, 13) (dual of [4194328, 4194194, 14]-code), using
  - constructionÂ X4 applied to C_e(12) âŠ‚ C_e(10) [i] based on
    1. linear OA(2¹³³, 4194304, F₂, 13) (dual of [4194304, 4194171, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 2²²âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    2. linear OA(2¹¹¹, 4194304, F₂, 11) (dual of [4194304, 4194193, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 2²²âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
    3. linear OA(2²³, 24, F₂, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,2)), using
      - dual of repetition code with length 24 [i]
    4. linear OA(2¹, 24, F₂, 1) (dual of [24, 23, 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, 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(2¹³⁵, 1048582, F₂, 8, 12) (dual of [(1048582, 8), 8388521, 13]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2¹³⁶, 1048582, F₂, 8, 12) (dual of [(1048582, 8), 8388520, 13]-NRT-code)	[i]
3	Linear OOA(2¹³⁷, 1048582, F₂, 8, 12) (dual of [(1048582, 8), 8388519, 13]-NRT-code)	[i]