MinT - Information on Result #1607369

Information on Result #1607369

Linear OOA(3¹⁸⁴, 56187, F₃, 4, 25) (dual of [(56187, 4), 224564, 26]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁸⁴, 56187, F₃, 3, 25) (dual of [(56187, 3), 168377, 26]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁸⁴, 59059, F₃, 3, 25) (dual of [(59059, 3), 176993, 26]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3¹⁸⁴, 177177, F₃, 25) (dual of [177177, 176993, 26]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(3¹⁸³, 177176, F₃, 25) (dual of [177176, 176993, 26]-code), using
    - constructionÂ X applied to C([0,12]) âŠ‚ C([0,10]) [i] based on
      1. linear OA(3¹⁷⁷, 177148, F₃, 25) (dual of [177148, 176971, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148Â | 3²²âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
      2. linear OA(3¹⁵⁵, 177148, F₃, 21) (dual of [177148, 176993, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148Â | 3²²âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
      3. linear OA(3⁶, 28, F₃, 3) (dual of [28, 22, 4]-code or 28-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(3¹⁸⁴, 18728, F₃, 28, 25) (dual of [(18728, 28), 524200, 26]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row