MinT - Information on Result #1663292

Information on Result #1663292

Linear OOA(2¹¹⁶, 104861, F₂, 6, 13) (dual of [(104861, 6), 629050, 14]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹¹⁶, 104861, F₂, 5, 13) (dual of [(104861, 5), 524189, 14]-NRT-code), using

OOA 5-folding [i] based on linear OA(2¹¹⁶, 524305, F₂, 13) (dual of [524305, 524189, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹¹⁶, 524308, F₂, 13) (dual of [524308, 524192, 14]-code), using
  - constructionÂ X applied to C_e(12) âŠ‚ C_e(10) [i] based on
    1. linear OA(2¹¹⁵, 524288, F₂, 13) (dual of [524288, 524173, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    2. linear OA(2⁹⁶, 524288, F₂, 11) (dual of [524288, 524192, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
    3. linear OA(2¹, 20, F₂, 1) (dual of [20, 19, 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(2¹¹⁶, 104860, F₂, 7, 13) (dual of [(104860, 7), 733904, 14]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹¹⁶, 104860, F₂, 8, 13) (dual of [(104860, 8), 838764, 14]-NRT-code)	[i]
3	Linear OOA(2¹¹⁶, 104860, F₂, 18, 13) (dual of [(104860, 18), 1887364, 14]-NRT-code)	[i]