MinT - Information on Result #1614936

Information on Result #1614936

Linear OOA(128⁶⁵, 4109, F₁₂₈, 4, 32) (dual of [(4109, 4), 16371, 33]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(128⁶⁵, 4109, F₁₂₈, 3, 32) (dual of [(4109, 3), 12262, 33]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(128⁶⁵, 5464, F₁₂₈, 3, 32) (dual of [(5464, 3), 16327, 33]-NRT-code), using
- OOA 3-folding [i] based on linear OA(128⁶⁵, 16392, F₁₂₈, 32) (dual of [16392, 16327, 33]-code), using
  - constructionÂ X applied to C_e(31) âŠ‚ C_e(28) [i] based on
    1. linear OA(128⁶³, 16384, F₁₂₈, 32) (dual of [16384, 16321, 33]-code), using an extension C_e(31) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,31], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 32 [i]
    2. linear OA(128⁵⁷, 16384, F₁₂₈, 29) (dual of [16384, 16327, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
    3. linear OA(128², 8, F₁₂₈, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,128)), using
      - discarding factors / shortening the dual code based on linear OA(128², 128, F₁₂₈, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
        Reedâ€“Solomon code RS(126,128) [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(128⁶⁵, 1027, F₁₂₈, 36, 32) (dual of [(1027, 36), 36907, 33]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row