MinT - Information on Result #1643565

Information on Result #1643565

Linear OOA(3¹³⁰, 22294, F₃, 5, 19) (dual of [(22294, 5), 111340, 20]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹³⁰, 22294, F₃, 2, 19) (dual of [(22294, 2), 44458, 20]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹³⁰, 29544, F₃, 2, 19) (dual of [(29544, 2), 58958, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹³⁰, 59088, F₃, 19) (dual of [59088, 58958, 20]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(3¹²⁹, 59087, F₃, 19) (dual of [59087, 58958, 20]-code), using
    - constructionÂ X applied to C_e(18) âŠ‚ C_e(13) [i] based on
      1. linear OA(3¹²¹, 59049, F₃, 19) (dual of [59049, 58928, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      2. linear OA(3⁹¹, 59049, F₃, 14) (dual of [59049, 58958, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
      3. linear OA(3⁸, 38, F₃, 4) (dual of [38, 30, 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(3¹³⁰, 11146, F₃, 25, 19) (dual of [(11146, 25), 278520, 20]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row