MinT - Information on Result #1082877

Information on Result #1082877

Linear OOA(128¹⁹, 699180, F₁₂₈, 4, 6) (dual of [(699180, 4), 2796701, 7]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(128³, 129, F₁₂₈, 4, 3) (dual of [(129, 4), 513, 4]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(4;513,128) [i]
linear OOA(128¹⁶, 699051, F₁₂₈, 4, 6) (dual of [(699051, 4), 2796188, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(128¹⁶, 2097153, F₁₂₈, 6) (dual of [2097153, 2097137, 7]-code), using
  - discarding factors / shortening the dual code based on linear OA(128¹⁶, 2097155, F₁₂₈, 6) (dual of [2097155, 2097139, 7]-code), using
    - constructionÂ X applied to C_e(5) âŠ‚ C_e(4) [i] based on
      1. linear OA(128¹⁶, 2097152, F₁₂₈, 6) (dual of [2097152, 2097136, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
      2. 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]
      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(128⁶⁴, 2796330, F₁₂₈, 4, 12) (dual of [(2796330, 4), 11185256, 13]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(128⁶⁸, 2796330, F₁₂₈, 4, 13) (dual of [(2796330, 4), 11185252, 14]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs