MinT - Information on Result #1700861

Information on Result #1700861

Linear OOA(2¹⁸⁰, 886, F₂, 8, 31) (dual of [(886, 8), 6908, 32]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁸⁰, 886, F₂, 2, 31) (dual of [(886, 2), 1592, 32]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁸⁰, 1047, F₂, 2, 31) (dual of [(1047, 2), 1914, 32]-NRT-code), using
- 2¹ times duplication [i] based on linear OOA(2¹⁷⁹, 1047, F₂, 2, 31) (dual of [(1047, 2), 1915, 32]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2¹⁷⁹, 2094, F₂, 31) (dual of [2094, 1915, 32]-code), using
    - constructionÂ X applied to C_e(30) âŠ‚ C_e(24) [i] based on
      1. linear OA(2¹⁶⁶, 2048, F₂, 31) (dual of [2048, 1882, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
      2. linear OA(2¹³³, 2048, F₂, 25) (dual of [2048, 1915, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
      3. linear OA(2¹³, 46, F₂, 5) (dual of [46, 33, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹³, 63, F₂, 5) (dual of [63, 50, 6]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [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(2¹⁸⁰, 442, F₂, 40, 31) (dual of [(442, 40), 17500, 32]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row