MinT - Information on Result #1613777

Information on Result #1613777

Linear OOA(81⁶¹, 2813, F₈₁, 4, 29) (dual of [(2813, 4), 11191, 30]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(81⁶¹, 2813, F₈₁, 2, 29) (dual of [(2813, 2), 5565, 30]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(81⁶¹, 3287, F₈₁, 2, 29) (dual of [(3287, 2), 6513, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(81⁶¹, 6574, F₈₁, 29) (dual of [6574, 6513, 30]-code), using
  - discarding factors / shortening the dual code based on linear OA(81⁶¹, 6575, F₈₁, 29) (dual of [6575, 6514, 30]-code), using
    - constructionÂ X applied to C_e(28) âŠ‚ C_e(23) [i] based on
      1. linear OA(81⁵⁷, 6561, F₈₁, 29) (dual of [6561, 6504, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [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(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(81⁶¹, 703, F₈₁, 36, 29) (dual of [(703, 36), 25247, 30]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row