MinT - Information on Result #904944

Information on Result #904944

Linear OOA(128⁴⁷, 1048706, F₁₂₈, 2, 14) (dual of [(1048706, 2), 2097365, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(128⁷, 129, F₁₂₈, 2, 7) (dual of [(129, 2), 251, 8]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;251,128) [i]
linear OOA(128⁴⁰, 1048577, F₁₂₈, 2, 14) (dual of [(1048577, 2), 2097114, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(128⁴⁰, 2097154, F₁₂₈, 14) (dual of [2097154, 2097114, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(128⁴⁰, 2097155, F₁₂₈, 14) (dual of [2097155, 2097115, 15]-code), using
    - constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
      1. 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]
      2. linear OA(128³⁷, 2097152, F₁₂₈, 13) (dual of [2097152, 2097115, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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(128⁴⁷, 524353, F₁₂₈, 4, 14) (dual of [(524353, 4), 2097365, 15]-NRT-code)	[i]		OOA Folding