MinT - Information on Result #1533635

Information on Result #1533635

Linear OOA(3²⁴⁹, 24487, F₃, 3, 36) (dual of [(24487, 3), 73212, 37]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁴⁹, 24487, F₃, 2, 36) (dual of [(24487, 2), 48725, 37]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²⁴⁹, 29545, F₃, 2, 36) (dual of [(29545, 2), 58841, 37]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3²⁴⁹, 59090, F₃, 36) (dual of [59090, 58841, 37]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²⁴⁹, 59091, F₃, 36) (dual of [59091, 58842, 37]-code), using
    - constructionÂ X applied to C([0,18]) âŠ‚ C([0,15]) [i] based on
      1. linear OA(3²⁴¹, 59050, F₃, 37) (dual of [59050, 58809, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 3²⁰âˆ’1, defining interval IÂ =Â [0,18], and minimum distance dÂ â‰¥ |{−18,−17,…,18}|+1Â =Â 38 (BCH-bound) [i]
      2. linear OA(3²⁰¹, 59050, F₃, 31) (dual of [59050, 58849, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 3²⁰âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]
      3. 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(3²⁴⁹, 12243, F₃, 5, 36) (dual of [(12243, 5), 60966, 37]-NRT-code)	[i]		OOA Folding