MinT - Information on Result #1613590

Information on Result #1613590

Linear OOA(81⁵¹, 3070, F₈₁, 4, 24) (dual of [(3070, 4), 12229, 25]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(81⁵¹, 3070, F₈₁, 2, 24) (dual of [(3070, 2), 6089, 25]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(81⁵¹, 3287, F₈₁, 2, 24) (dual of [(3287, 2), 6523, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(81⁵¹, 6574, F₈₁, 24) (dual of [6574, 6523, 25]-code), using
  - discarding factors / shortening the dual code based on linear OA(81⁵¹, 6575, F₈₁, 24) (dual of [6575, 6524, 25]-code), using
    - constructionÂ X applied to C_e(23) âŠ‚ C_e(18) [i] based on
      1. 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]
      2. linear OA(81³⁷, 6561, F₈₁, 19) (dual of [6561, 6524, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      3. linear OA(81⁴, 14, F₈₁, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,81)), using
        discarding factors / shortening the dual code based on linear OA(81⁴, 81, F₈₁, 4) (dual of [81, 77, 5]-code or 81-arc in PG(3,81)), using
        Reedâ€“Solomon code RS(77,81) [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(81⁵¹, 1023, F₈₁, 28, 24) (dual of [(1023, 28), 28593, 25]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row