MinT - Information on Result #1698673

Information on Result #1698673

Linear OOA(2¹⁴¹, 209719, F₂, 8, 14) (dual of [(209719, 8), 1677611, 15]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁴¹, 209719, F₂, 5, 14) (dual of [(209719, 5), 1048454, 15]-NRT-code), using

OOA 5-folding [i] based on linear OA(2¹⁴¹, 1048595, F₂, 14) (dual of [1048595, 1048454, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹⁴¹, 1048597, F₂, 14) (dual of [1048597, 1048456, 15]-code), using
  - 1 times truncation [i] based on linear OA(2¹⁴², 1048598, F₂, 15) (dual of [1048598, 1048456, 16]-code), using
    - constructionÂ X4 applied to C_e(14) âŠ‚ C_e(12) [i] based on
      1. linear OA(2¹⁴¹, 1048576, F₂, 15) (dual of [1048576, 1048435, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 2²⁰âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
      2. linear OA(2¹²¹, 1048576, F₂, 13) (dual of [1048576, 1048455, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 2²⁰âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      3. linear OA(2²¹, 22, F₂, 21) (dual of [22, 1, 22]-code or 22-arc in PG(20,2)), using
        dual of repetition code with length 22 [i]
      4. linear OA(2¹, 22, F₂, 1) (dual of [22, 21, 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(2¹⁴², 209719, F₂, 8, 14) (dual of [(209719, 8), 1677610, 15]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2¹⁴³, 209719, F₂, 8, 14) (dual of [(209719, 8), 1677609, 15]-NRT-code)	[i]		OOA Duplication