MinT - Information on Result #1523212

Information on Result #1523212

Linear OOA(3¹³⁰, 29549, F₃, 3, 18) (dual of [(29549, 3), 88517, 19]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹³⁰, 29549, F₃, 2, 18) (dual of [(29549, 2), 58968, 19]-NRT-code), using

OOA 2-folding [i] based on linear OA(3¹³⁰, 59098, F₃, 18) (dual of [59098, 58968, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(3¹³⁰, 59099, F₃, 18) (dual of [59099, 58969, 19]-code), using
  - constructionÂ X applied to C([0,9]) âŠ‚ C([0,6]) [i] based on
    1. linear OA(3¹²¹, 59050, F₃, 19) (dual of [59050, 58929, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 3²⁰âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
    2. linear OA(3⁸¹, 59050, F₃, 13) (dual of [59050, 58969, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 3²⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
    3. linear OA(3⁹, 49, F₃, 4) (dual of [49, 40, 5]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁹, 80, F₃, 4) (dual of [80, 71, 5]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [0,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [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(3¹³⁰, 14774, F₃, 5, 18) (dual of [(14774, 5), 73740, 19]-NRT-code)	[i]		OOA Folding