MinT - Information on Result #1418715

Information on Result #1418715

Linear OOA(3²⁴⁰, 6423, F₃, 2, 41) (dual of [(6423, 2), 12606, 42]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3²⁴⁰, 6423, F₃, 41) (dual of [6423, 6183, 42]-code), using

discarding factors / shortening the dual code based on linear OA(3²⁴⁰, 6632, F₃, 41) (dual of [6632, 6392, 42]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3²³⁸, 6630, F₃, 41) (dual of [6630, 6392, 42]-code), using
  - constructionÂ X applied to C_e(40) âŠ‚ C_e(31) [i] based on
    1. linear OA(3²¹⁷, 6561, F₃, 41) (dual of [6561, 6344, 42]-code), using an extension C_e(40) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,40], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 41 [i]
    2. linear OA(3¹⁶⁹, 6561, F₃, 32) (dual of [6561, 6392, 33]-code), using an extension C_e(31) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,31], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 32 [i]
    3. linear OA(3²¹, 69, F₃, 8) (dual of [69, 48, 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, 3211, F₃, 3, 41) (dual of [(3211, 3), 9393, 42]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3²⁴⁰, 3211, F₃, 4, 41) (dual of [(3211, 4), 12604, 42]-NRT-code)	[i]		OOA Folding