MinT - Information on Result #1833943

Information on Result #1833943

OOA(8⁴⁰, 1398106, S₈, 3, 6), using OOA 3-folding based on OA(8⁴⁰, 4194318, S₈, 6), using

discarding factors based on OA(8⁴⁰, 4194320, S₈, 6), using
- trace code [i] based on OA(64²⁰, 2097160, S₆₄, 6), using
  - discarding parts of the base [i] based on linear OA(128¹⁷, 2097160, F₁₂₈, 6) (dual of [2097160, 2097143, 7]-code), using
    - constructionÂ X4 applied to C_e(5) âŠ‚ C_e(3) [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(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(128⁷, 8, F₁₂₈, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,128)), using
        dual of repetition code with length 8 [i]
      4. linear OA(128¹, 8, F₁₂₈, 1) (dual of [8, 7, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(128¹, 128, F₁₂₈, 1) (dual of [128, 127, 2]-code), using
        Reedâ€“Solomon code RS(127,128) [i]

Mode: Constructive.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	OOA(8¹³⁰, 6990508, S₈, 3, 12)	[i]		(u,Â u+v)-Construction for OOAs
2	OOA(8¹³⁸, 6990508, S₈, 3, 13)	[i]		(u,Â u+v)-Construction for OOAs