MinT - Information on Result #1681583

Information on Result #1681583

Linear OOA(2¹⁴², 174766, F₂, 7, 15) (dual of [(174766, 7), 1223220, 16]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁴², 174766, F₂, 6, 15) (dual of [(174766, 6), 1048454, 16]-NRT-code), using

OOA 6-folding [i] based on linear OA(2¹⁴², 1048596, F₂, 15) (dual of [1048596, 1048454, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹⁴², 1048597, F₂, 15) (dual of [1048597, 1048455, 16]-code), using
  - constructionÂ X 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(2¹, 21, F₂, 1) (dual of [21, 20, 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(2¹⁴³, 174766, F₂, 7, 15) (dual of [(174766, 7), 1223219, 16]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2¹⁴², 174765, F₂, 8, 15) (dual of [(174765, 8), 1397978, 16]-NRT-code)	[i]		OOA Stacking with Additional Row
3	Linear OOA(2¹⁴², 174765, F₂, 21, 15) (dual of [(174765, 21), 3669923, 16]-NRT-code)	[i]		OOA Stacking with Additional Row