MinT - Information on Result #1521468

Information on Result #1521468

Linear OOA(3⁸⁸, 28711, F₃, 3, 13) (dual of [(28711, 3), 86045, 14]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3⁸⁸, 28711, F₃, 2, 13) (dual of [(28711, 2), 57334, 14]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3⁸⁸, 29538, F₃, 2, 13) (dual of [(29538, 2), 58988, 14]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3⁸⁷, 29538, F₃, 2, 13) (dual of [(29538, 2), 58989, 14]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3⁸⁷, 59076, F₃, 13) (dual of [59076, 58989, 14]-code), using
    - constructionÂ X applied to C([0,6]) âŠ‚ C([0,4]) [i] based on
      1. 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]
      2. linear OA(3⁶¹, 59050, F₃, 9) (dual of [59050, 58989, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 3²⁰âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
      3. linear OA(3⁶, 26, F₃, 3) (dual of [26, 20, 4]-code or 26-cap in PG(5,3)), using
        discarding factors / shortening the dual code based on linear OA(3⁶, 48, F₃, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
        large caps in PG(5,Â b) [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(3⁸⁸, 14355, F₃, 5, 13) (dual of [(14355, 5), 71687, 14]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3⁸⁸, 14355, F₃, 15, 13) (dual of [(14355, 15), 215237, 14]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row