MinT - Information on Result #904881

Information on Result #904881

Linear OOA(128⁴⁰, 1048706, F₁₂₈, 2, 12) (dual of [(1048706, 2), 2097372, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(128⁶, 129, F₁₂₈, 2, 6) (dual of [(129, 2), 252, 7]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;252,128) [i]
linear OOA(128³⁴, 1048577, F₁₂₈, 2, 12) (dual of [(1048577, 2), 2097120, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(128³⁴, 2097154, F₁₂₈, 12) (dual of [2097154, 2097120, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(128³⁴, 2097155, F₁₂₈, 12) (dual of [2097155, 2097121, 13]-code), using
    - constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
      1. linear OA(128³⁴, 2097152, F₁₂₈, 12) (dual of [2097152, 2097118, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
      2. linear OA(128³¹, 2097152, F₁₂₈, 11) (dual of [2097152, 2097121, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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(128⁴⁰, 524353, F₁₂₈, 4, 12) (dual of [(524353, 4), 2097372, 13]-NRT-code)	[i]		OOA Folding