MinT - Information on Result #904761

Information on Result #904761

Linear OOA(128¹⁵, 1048706, F₁₂₈, 2, 5) (dual of [(1048706, 2), 2097397, 6]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(128², 129, F₁₂₈, 2, 2) (dual of [(129, 2), 256, 3]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;256,128) [i]
linear OOA(128¹³, 1048577, F₁₂₈, 2, 5) (dual of [(1048577, 2), 2097141, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(128¹³, 2097154, F₁₂₈, 5) (dual of [2097154, 2097141, 6]-code), using
  - discarding factors / shortening the dual code based on linear OA(128¹³, 2097155, F₁₂₈, 5) (dual of [2097155, 2097142, 6]-code), using
    - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
      1. linear OA(128¹³, 2097152, F₁₂₈, 5) (dual of [2097152, 2097139, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
      2. linear OA(128¹⁰, 2097152, F₁₂₈, 4) (dual of [2097152, 2097142, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [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(128⁵², 5243007, F₁₂₈, 2, 10) (dual of [(5243007, 2), 10485962, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(128⁵⁶, 5243007, F₁₂₈, 2, 11) (dual of [(5243007, 2), 10485958, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs