MinT - Information on Result #1530227

Information on Result #1530227

Linear OOA(3²²¹, 7978, F₃, 3, 37) (dual of [(7978, 3), 23713, 38]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²²¹, 7978, F₃, 2, 37) (dual of [(7978, 2), 15735, 38]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²²¹, 9852, F₃, 2, 37) (dual of [(9852, 2), 19483, 38]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3²²¹, 19704, F₃, 37) (dual of [19704, 19483, 38]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²²¹, 19705, F₃, 37) (dual of [19705, 19484, 38]-code), using
    - constructionÂ X applied to C_e(36) âŠ‚ C_e(33) [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(3¹⁹⁹, 19683, F₃, 34) (dual of [19683, 19484, 35]-code), using an extension C_e(33) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,33], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [i]
      3. linear OA(3⁴, 22, F₃, 2) (dual of [22, 18, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
        Hamming code H(4,3) [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(3²²¹, 3989, F₃, 5, 37) (dual of [(3989, 5), 19724, 38]-NRT-code)	[i]		OOA Folding