MinT - Information on Result #1529908

Information on Result #1529908

Linear OOA(3²¹⁸, 4569, F₃, 3, 39) (dual of [(4569, 3), 13489, 40]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3²¹⁸, 4569, F₃, 39) (dual of [4569, 4351, 40]-code), using

discarding factors / shortening the dual code based on linear OA(3²¹⁸, 6602, F₃, 39) (dual of [6602, 6384, 40]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3²¹⁷, 6601, F₃, 39) (dual of [6601, 6384, 40]-code), using
  - constructionÂ X applied to C_e(39) âŠ‚ C_e(33) [i] based on
    1. linear OA(3²⁰⁹, 6561, F₃, 40) (dual of [6561, 6352, 41]-code), using an extension C_e(39) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,39], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 40 [i]
    2. linear OA(3¹⁷⁷, 6561, F₃, 34) (dual of [6561, 6384, 35]-code), using an extension C_e(33) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,33], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [i]
    3. linear OA(3⁸, 40, F₃, 4) (dual of [40, 32, 5]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁸, 41, F₃, 4) (dual of [41, 33, 5]-code), using
        the narrow-sense BCH-code C(I) with length 41Â | 3⁸âˆ’1, defining interval IÂ =Â [1,1], and minimum distance dÂ â‰¥ |{−3,−1,1,3}|+1Â =Â 5 (BCH-bound) [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(3²¹⁸, 2284, F₃, 5, 39) (dual of [(2284, 5), 11202, 40]-NRT-code)	[i]		OOA Folding