MinT - Information on Result #1848799

Information on Result #1848799

OOA(64³⁴, 1048579, S₆₄, 3, 10), using discarding parts of the base based on linear OOA(128²⁹, 1048579, F₁₂₈, 3, 10) (dual of [(1048579, 3), 3145708, 11]-NRT-code), using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(128²⁹, 1048579, F₁₂₈, 2, 10) (dual of [(1048579, 2), 2097129, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(128²⁹, 2097158, F₁₂₈, 10) (dual of [2097158, 2097129, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(128²⁹, 2097159, F₁₂₈, 10) (dual of [2097159, 2097130, 11]-code), using
    - constructionÂ X applied to C_e(9) âŠ‚ C_e(7) [i] based on
      1. linear OA(128²⁸, 2097152, F₁₂₈, 10) (dual of [2097152, 2097124, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
      2. linear OA(128²², 2097152, F₁₂₈, 8) (dual of [2097152, 2097130, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [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: Arbitrary.

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(64³⁴, 524289, S₆₄, 15, 10)	[i]		OOA Folding and Stacking with Additional Row