MinT - Information on Result #1614897

Information on Result #1614897

Linear OOA(128⁶³, 7288, F₁₂₈, 4, 29) (dual of [(7288, 4), 29089, 30]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(128⁶³, 7288, F₁₂₈, 2, 29) (dual of [(7288, 2), 14513, 30]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(128⁶³, 8202, F₁₂₈, 2, 29) (dual of [(8202, 2), 16341, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(128⁶³, 16404, F₁₂₈, 29) (dual of [16404, 16341, 30]-code), using
  - constructionÂ X applied to C_e(28) âŠ‚ C_e(21) [i] based on
    1. 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]
    2. linear OA(128⁴³, 16384, F₁₂₈, 22) (dual of [16384, 16341, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [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(128⁶³, 1821, F₁₂₈, 36, 29) (dual of [(1821, 36), 65493, 30]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row