MinT - Information on Result #1613718

Information on Result #1613718

Linear OOA(81⁵⁸, 2385, F₈₁, 4, 28) (dual of [(2385, 4), 9482, 29]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(81⁵⁸, 2385, F₈₁, 2, 28) (dual of [(2385, 2), 4712, 29]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(81⁵⁸, 3286, F₈₁, 2, 28) (dual of [(3286, 2), 6514, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(81⁵⁸, 6572, F₈₁, 28) (dual of [6572, 6514, 29]-code), using
  - constructionÂ X applied to C_e(27) âŠ‚ C_e(23) [i] based on
    1. linear OA(81⁵⁵, 6561, F₈₁, 28) (dual of [6561, 6506, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
    2. linear OA(81⁴⁷, 6561, F₈₁, 24) (dual of [6561, 6514, 25]-code), using an extension C_e(23) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,23], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]
    3. linear OA(81³, 11, F₈₁, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,81) or 11-cap in PG(2,81)), using
      - discarding factors / shortening the dual code based on linear OA(81³, 81, F₈₁, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
        Reedâ€“Solomon code RS(78,81) [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(81⁵⁸, 596, F₈₁, 36, 28) (dual of [(596, 36), 21398, 29]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row