MinT - Information on Result #1614549

Information on Result #1614549

Linear OOA(128⁴³, 5124, F₁₂₈, 4, 21) (dual of [(5124, 4), 20453, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(128⁴³, 5124, F₁₂₈, 3, 21) (dual of [(5124, 3), 15329, 22]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(128⁴³, 5464, F₁₂₈, 3, 21) (dual of [(5464, 3), 16349, 22]-NRT-code), using
- OOA 3-folding [i] based on linear OA(128⁴³, 16392, F₁₂₈, 21) (dual of [16392, 16349, 22]-code), using
  - constructionÂ X applied to C_e(20) âŠ‚ C_e(17) [i] based on
    1. 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]
    2. linear OA(128³⁵, 16384, F₁₂₈, 18) (dual of [16384, 16349, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [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(128⁴³, 1707, F₁₂₈, 28, 21) (dual of [(1707, 28), 47753, 22]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row