MinT - Information on Result #1532470

Information on Result #1532470

Linear OOA(3²⁴⁰, 12564, F₃, 3, 37) (dual of [(12564, 3), 37452, 38]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3²⁴⁰, 12564, F₃, 37) (dual of [12564, 12324, 38]-code), using

discarding factors / shortening the dual code based on linear OA(3²⁴⁰, 19760, F₃, 37) (dual of [19760, 19520, 38]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3²³⁸, 19758, F₃, 37) (dual of [19758, 19520, 38]-code), using
  - constructionÂ X applied to C_e(36) âŠ‚ C_e(27) [i] based on
    1. linear OA(3²¹⁷, 19683, F₃, 37) (dual of [19683, 19466, 38]-code), using an extension C_e(36) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [i]
    2. linear OA(3¹⁶³, 19683, F₃, 28) (dual of [19683, 19520, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
    3. linear OA(3²¹, 75, F₃, 8) (dual of [75, 54, 9]-code), using
      - discarding factors / shortening the dual code based on linear OA(3²¹, 80, F₃, 8) (dual of [80, 59, 9]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]

Mode: Linear.

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	Linear OOA(3²⁴⁰, 6282, F₃, 5, 37) (dual of [(6282, 5), 31170, 38]-NRT-code)	[i]		OOA Folding