MinT - Information on Result #1836689

Information on Result #1836689

OOA(9¹²², 5598964, S₉, 3, 13), using (u,Â u+v)-construction based on

OOA(9²⁴, 6562, S₉, 3, 6), using
- OOA 3-folding [i] based on OA(9²⁴, 19686, S₉, 6), using
  - discarding parts of the base [i] based on linear OA(27¹⁶, 19686, F₂₇, 6) (dual of [19686, 19670, 7]-code), using
    - constructionÂ X applied to C_e(5) âŠ‚ C_e(4) [i] based on
      1. linear OA(27¹⁶, 19683, F₂₇, 6) (dual of [19683, 19667, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
      2. linear OA(27¹³, 19683, F₂₇, 5) (dual of [19683, 19670, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
      3. linear OA(27⁰, 3, F₂₇, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(27⁰, s, F₂₇, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
linear OOA(9⁹⁸, 5592402, F₉, 3, 13) (dual of [(5592402, 3), 16777108, 14]-NRT-code), using
- trace code [i] based on linear OOA(81⁴⁹, 2796201, F₈₁, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(81⁴⁹, large, F₈₁, 13) (dual of [large, large−49, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [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(9¹²³, 5598964, S₉, 3, 13)	[i]		OOA Duplication