MinT - Information on Result #1531236

Information on Result #1531236

Linear OOA(3²³⁰, 25432, F₃, 3, 33) (dual of [(25432, 3), 76066, 34]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²³⁰, 25432, F₃, 2, 33) (dual of [(25432, 2), 50634, 34]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²³⁰, 29549, F₃, 2, 33) (dual of [(29549, 2), 58868, 34]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3²³⁰, 59098, F₃, 33) (dual of [59098, 58868, 34]-code), using
  - constructionÂ X applied to C_e(33) âŠ‚ C_e(27) [i] based on
    1. linear OA(3²²¹, 59049, F₃, 34) (dual of [59049, 58828, 35]-code), using an extension C_e(33) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,33], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [i]
    2. linear OA(3¹⁸¹, 59049, F₃, 28) (dual of [59049, 58868, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [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(3²³⁰, 12716, F₃, 5, 33) (dual of [(12716, 5), 63350, 34]-NRT-code)	[i]		OOA Folding