MinT - Information on Result #1537874

Information on Result #1537874

Linear OOA(4¹⁵⁰, 1866242, F₄, 3, 18) (dual of [(1866242, 3), 5598576, 19]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹⁵⁰, 1866242, F₄, 2, 18) (dual of [(1866242, 2), 3732334, 19]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹⁵⁰, 2097171, F₄, 2, 18) (dual of [(2097171, 2), 4194192, 19]-NRT-code), using
- 4¹ times duplication [i] based on linear OOA(4¹⁴⁹, 2097171, F₄, 2, 18) (dual of [(2097171, 2), 4194193, 19]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4¹⁴⁹, 4194342, F₄, 18) (dual of [4194342, 4194193, 19]-code), using
    - constructionÂ X applied to C_e(17) âŠ‚ C_e(13) [i] based on
      1. linear OA(4¹⁴⁴, 4194304, F₄, 18) (dual of [4194304, 4194160, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
      2. linear OA(4¹¹¹, 4194304, F₄, 14) (dual of [4194304, 4194193, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
      3. linear OA(4⁵, 38, F₄, 3) (dual of [38, 33, 4]-code or 38-cap in PG(4,4)), using
        discarding factors / shortening the dual code based on linear OA(4⁵, 41, F₄, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
        a cap found by Tallinii [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(4¹⁵⁰, 622080, F₄, 21, 18) (dual of [(622080, 21), 13063530, 19]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row