MinT - Information on Result #905114

Information on Result #905114

Linear OOA(128⁶⁸, 1048706, F₁₂₈, 2, 20) (dual of [(1048706, 2), 2097344, 21]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(128¹⁰, 129, F₁₂₈, 2, 10) (dual of [(129, 2), 248, 11]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;248,128) [i]
linear OOA(128⁵⁸, 1048577, F₁₂₈, 2, 20) (dual of [(1048577, 2), 2097096, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(128⁵⁸, 2097154, F₁₂₈, 20) (dual of [2097154, 2097096, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(128⁵⁸, 2097155, F₁₂₈, 20) (dual of [2097155, 2097097, 21]-code), using
    - constructionÂ X applied to C_e(19) âŠ‚ C_e(18) [i] based on
      1. linear OA(128⁵⁸, 2097152, F₁₂₈, 20) (dual of [2097152, 2097094, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      2. linear OA(128⁵⁵, 2097152, F₁₂₈, 19) (dual of [2097152, 2097097, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(128⁶⁸, 524353, F₁₂₈, 4, 20) (dual of [(524353, 4), 2097344, 21]-NRT-code)	[i]		OOA Folding
2	Linear OOA(128⁶⁸, 209741, F₁₂₈, 22, 20) (dual of [(209741, 22), 4614234, 21]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row