MinT - Information on Result #1613540

Information on Result #1613540

Linear OOA(81⁴⁸, 2034, F₈₁, 4, 24) (dual of [(2034, 4), 8088, 25]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(81⁴⁸, 2034, F₈₁, 3, 24) (dual of [(2034, 3), 6054, 25]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(81⁴⁸, 2188, F₈₁, 3, 24) (dual of [(2188, 3), 6516, 25]-NRT-code), using
- OOA 3-folding [i] based on linear OA(81⁴⁸, 6564, F₈₁, 24) (dual of [6564, 6516, 25]-code), using
  - discarding factors / shortening the dual code based on linear OA(81⁴⁸, 6566, F₈₁, 24) (dual of [6566, 6518, 25]-code), using
    - constructionÂ X applied to C_e(23) âŠ‚ C_e(21) [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(81⁴³, 6561, F₈₁, 22) (dual of [6561, 6518, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      3. linear OA(81¹, 5, F₈₁, 1) (dual of [5, 4, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(81¹, s, F₈₁, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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(81⁴⁸, 677, F₈₁, 28, 24) (dual of [(677, 28), 18908, 25]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row