MinT - Information on Result #1614878

Information on Result #1614878

Linear OOA(128⁶², 8203, F₁₂₈, 4, 28) (dual of [(8203, 4), 32750, 29]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(128⁶², 8203, F₁₂₈, 2, 28) (dual of [(8203, 2), 16344, 29]-NRT-code), using

OOA 2-folding [i] based on linear OA(128⁶², 16406, F₁₂₈, 28) (dual of [16406, 16344, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(128⁶², 16407, F₁₂₈, 28) (dual of [16407, 16345, 29]-code), using
  - constructionÂ X applied to C_e(27) âŠ‚ C_e(19) [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(128³⁹, 16384, F₁₂₈, 20) (dual of [16384, 16345, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
    3. linear OA(128⁷, 23, F₁₂₈, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,128)), using
      - discarding factors / shortening the dual code based on linear OA(128⁷, 128, F₁₂₈, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
        Reedâ€“Solomon code RS(121,128) [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(128⁶², 2050, F₁₂₈, 36, 28) (dual of [(2050, 36), 73738, 29]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row