MinT - Information on Result #1566380

Information on Result #1566380

Linear OOA(128²⁰, 6974, F₁₂₈, 3, 10) (dual of [(6974, 3), 20902, 11]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(128²⁰, 6974, F₁₂₈, 2, 10) (dual of [(6974, 2), 13928, 11]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(128²⁰, 8194, F₁₂₈, 2, 10) (dual of [(8194, 2), 16368, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(128²⁰, 16388, F₁₂₈, 10) (dual of [16388, 16368, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(128²⁰, 16389, F₁₂₈, 10) (dual of [16389, 16369, 11]-code), using
    - constructionÂ X applied to C_e(9) âŠ‚ C_e(7) [i] based on
      1. linear OA(128¹⁹, 16384, F₁₂₈, 10) (dual of [16384, 16365, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
      2. linear OA(128¹⁵, 16384, F₁₂₈, 8) (dual of [16384, 16369, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      3. linear OA(128¹, 5, F₁₂₈, 1) (dual of [5, 4, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(128¹, s, F₁₂₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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	OOA(64²⁴, 6974, S₆₄, 3, 10)	[i]		Discarding Parts of the Base for OOAs
2	Linear OOA(128²⁰, 3486, F₁₂₈, 15, 10) (dual of [(3486, 15), 52270, 11]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row