MinT - Information on Result #1418289

Information on Result #1418289

Linear OOA(3²³⁶, 13401, F₃, 2, 36) (dual of [(13401, 2), 26566, 37]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3²³⁶, 13401, F₃, 36) (dual of [13401, 13165, 37]-code), using

discarding factors / shortening the dual code based on linear OA(3²³⁶, 19756, F₃, 36) (dual of [19756, 19520, 37]-code), using
- 3 times code embedding in larger space [i] based on linear OA(3²³³, 19753, F₃, 36) (dual of [19753, 19520, 37]-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(3¹⁶, 70, F₃, 7) (dual of [70, 54, 8]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹⁶, 82, F₃, 7) (dual of [82, 66, 8]-code), using
        generator matrices provided on Edelâ€™s homepage [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(3²³⁶, 6700, F₃, 3, 36) (dual of [(6700, 3), 19864, 37]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3²³⁶, 6700, F₃, 4, 36) (dual of [(6700, 4), 26564, 37]-NRT-code)	[i]		OOA Folding