MinT - Information on Result #1613625

Information on Result #1613625

Linear OOA(81⁵³, 2996, F₈₁, 4, 25) (dual of [(2996, 4), 11931, 26]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(81⁵³, 2996, F₈₁, 2, 25) (dual of [(2996, 2), 5939, 26]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(81⁵³, 3287, F₈₁, 2, 25) (dual of [(3287, 2), 6521, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(81⁵³, 6574, F₈₁, 25) (dual of [6574, 6521, 26]-code), using
  - discarding factors / shortening the dual code based on linear OA(81⁵³, 6575, F₈₁, 25) (dual of [6575, 6522, 26]-code), using
    - constructionÂ X applied to C_e(24) âŠ‚ C_e(19) [i] based on
      1. linear OA(81⁴⁹, 6561, F₈₁, 25) (dual of [6561, 6512, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
      2. linear OA(81³⁹, 6561, F₈₁, 20) (dual of [6561, 6522, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [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(81⁵³, 998, F₈₁, 28, 25) (dual of [(998, 28), 27891, 26]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row