MinT - Information on Result #1699554

Information on Result #1699554

Linear OOA(2¹⁵⁸, 838866, F₂, 8, 14) (dual of [(838866, 8), 6710770, 15]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁵⁸, 838866, F₂, 5, 14) (dual of [(838866, 5), 4194172, 15]-NRT-code), using

OOA 5-folding [i] based on linear OA(2¹⁵⁸, 4194330, F₂, 14) (dual of [4194330, 4194172, 15]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2¹⁵⁵, 4194327, F₂, 14) (dual of [4194327, 4194172, 15]-code), using
  - 1 times truncation [i] based on linear OA(2¹⁵⁶, 4194328, F₂, 15) (dual of [4194328, 4194172, 16]-code), using
    - constructionÂ X4 applied to C_e(14) âŠ‚ C_e(12) [i] based on
      1. linear OA(2¹⁵⁵, 4194304, F₂, 15) (dual of [4194304, 4194149, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 2²²âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
      2. 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]
      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, 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(2¹⁵⁹, 838866, F₂, 8, 14) (dual of [(838866, 8), 6710769, 15]-NRT-code)	[i]		OOA Duplication