MinT - Information on Result #1746887

Information on Result #1746887

Linear OOA(128²⁵, 1048576, F₁₂₈, 12, 9) (dual of [(1048576, 12), 12582887, 10]-NRT-code), using OOA stacking with additional row based on linear OOA(128²⁵, 1048577, F₁₂₈, 4, 9) (dual of [(1048577, 4), 4194283, 10]-NRT-code), using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(128²⁵, 1048577, F₁₂₈, 2, 9) (dual of [(1048577, 2), 2097129, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(128²⁵, 2097154, F₁₂₈, 9) (dual of [2097154, 2097129, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(128²⁵, 2097155, F₁₂₈, 9) (dual of [2097155, 2097130, 10]-code), using
    - constructionÂ X applied to C_e(8) âŠ‚ C_e(7) [i] based on
      1. linear OA(128²⁵, 2097152, F₁₂₈, 9) (dual of [2097152, 2097127, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [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(128⁰, 3, F₁₂₈, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(128⁰, s, F₁₂₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Linear.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (16, 25, 1048576)-net over F₁₂₈	[i]		Net Defined by OOA