MinT - Information on Result #1614859

Information on Result #1614859

Linear OOA(128⁶¹, 7519, F₁₂₈, 4, 28) (dual of [(7519, 4), 30015, 29]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(128⁶¹, 7519, F₁₂₈, 2, 28) (dual of [(7519, 2), 14977, 29]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(128⁶¹, 8202, F₁₂₈, 2, 28) (dual of [(8202, 2), 16343, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(128⁶¹, 16404, F₁₂₈, 28) (dual of [16404, 16343, 29]-code), using
  - constructionÂ X applied to C_e(27) âŠ‚ C_e(20) [i] based on
    1. linear OA(128⁵⁵, 16384, F₁₂₈, 28) (dual of [16384, 16329, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
    2. linear OA(128⁴¹, 16384, F₁₂₈, 21) (dual of [16384, 16343, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
    3. linear OA(128⁶, 20, F₁₂₈, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,128)), using
      - discarding factors / shortening the dual code based on linear OA(128⁶, 128, F₁₂₈, 6) (dual of [128, 122, 7]-code or 128-arc in PG(5,128)), using
        Reedâ€“Solomon code RS(122,128) [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(128⁶¹, 1879, F₁₂₈, 36, 28) (dual of [(1879, 36), 67583, 29]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row