MinT - Information on Result #1540833

Information on Result #1540833

Linear OOA(4¹⁹⁴, 131087, F₄, 3, 28) (dual of [(131087, 3), 393067, 29]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹⁹⁴, 131087, F₄, 2, 28) (dual of [(131087, 2), 261980, 29]-NRT-code), using

OOA 2-folding [i] based on linear OA(4¹⁹⁴, 262174, F₄, 28) (dual of [262174, 261980, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(4¹⁹⁴, 262175, F₄, 28) (dual of [262175, 261981, 29]-code), using
  - 1 times truncation [i] based on linear OA(4¹⁹⁵, 262176, F₄, 29) (dual of [262176, 261981, 30]-code), using
    - constructionÂ X applied to C_e(28) âŠ‚ C_e(24) [i] based on
      1. linear OA(4¹⁹⁰, 262144, F₄, 29) (dual of [262144, 261954, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
      2. linear OA(4¹⁶³, 262144, F₄, 25) (dual of [262144, 261981, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
      3. linear OA(4⁵, 32, F₄, 3) (dual of [32, 27, 4]-code or 32-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(4¹⁹⁴, 26217, F₄, 33, 28) (dual of [(26217, 33), 864967, 29]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row