MinT - Information on Result #1613327

Information on Result #1613327

Linear OOA(81³¹, 2702, F₈₁, 4, 15) (dual of [(2702, 4), 10777, 16]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(81³¹, 2702, F₈₁, 2, 15) (dual of [(2702, 2), 5373, 16]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(81³¹, 3284, F₈₁, 2, 15) (dual of [(3284, 2), 6537, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(81³¹, 6568, F₈₁, 15) (dual of [6568, 6537, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(81³¹, 6569, F₈₁, 15) (dual of [6569, 6538, 16]-code), using
    - constructionÂ X applied to C_e(14) âŠ‚ C_e(11) [i] based on
      1. linear OA(81²⁹, 6561, F₈₁, 15) (dual of [6561, 6532, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
      2. linear OA(81²³, 6561, F₈₁, 12) (dual of [6561, 6538, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
      3. linear OA(81², 8, F₈₁, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,81)), using
        discarding factors / shortening the dual code based on linear OA(81², 81, F₈₁, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
        Reedâ€“Solomon code RS(79,81) [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(81³¹, 1350, F₈₁, 20, 15) (dual of [(1350, 20), 26969, 16]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row