MinT - Information on Result #1566653

Information on Result #1566653

Linear OOA(128⁴⁷, 878594, F₁₂₈, 3, 16) (dual of [(878594, 3), 2635735, 17]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(128⁴⁷, 878594, F₁₂₈, 2, 16) (dual of [(878594, 2), 1757141, 17]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(128⁴⁷, 1048579, F₁₂₈, 2, 16) (dual of [(1048579, 2), 2097111, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(128⁴⁷, 2097158, F₁₂₈, 16) (dual of [2097158, 2097111, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(128⁴⁷, 2097159, F₁₂₈, 16) (dual of [2097159, 2097112, 17]-code), using
    - constructionÂ X applied to C_e(15) âŠ‚ C_e(13) [i] based on
      1. linear OA(128⁴⁶, 2097152, F₁₂₈, 16) (dual of [2097152, 2097106, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
      2. linear OA(128⁴⁰, 2097152, F₁₂₈, 14) (dual of [2097152, 2097112, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
      3. linear OA(128¹, 7, F₁₂₈, 1) (dual of [7, 6, 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(64⁵⁵, 878594, S₆₄, 3, 16)	[i]		Discarding Parts of the Base for OOAs