MinT - Information on Result #1836991

Information on Result #1836991

OOA(128⁵⁴, 2801663, S₁₂₈, 3, 13), using (u,Â u+v)-construction based on

linear OOA(128¹¹, 5462, F₁₂₈, 3, 6) (dual of [(5462, 3), 16375, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(128¹¹, 16386, F₁₂₈, 6) (dual of [16386, 16375, 7]-code), using
  - constructionÂ X applied to C_e(5) âŠ‚ C_e(4) [i] based on
    1. linear OA(128¹¹, 16384, F₁₂₈, 6) (dual of [16384, 16373, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
    2. linear OA(128⁹, 16384, F₁₂₈, 5) (dual of [16384, 16375, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
    3. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 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]
OOA(128⁴³, 2796201, S₁₂₈, 3, 13), using
- OOA 3-folding [i] based on OA(128⁴³, large, S₁₂₈, 13), using
  - discarding parts of the base [i] based on linear OA(256³⁷, large, F₂₅₆, 13) (dual of [large, large−37, 14]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]

Mode: Constructive.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	OOA(128⁷³, 5597864, S₁₂₈, 3, 13)	[i]		(u,Â u+v)-Construction for OOAs
2	OOA(128⁷⁷, 5603326, S₁₂₈, 3, 13)	[i]		(u,Â u+v)-Construction for OOAs