MinT - Information on Result #1645123

Information on Result #1645123

Linear OOA(3¹⁵⁸, 59058, F₃, 5, 21) (dual of [(59058, 5), 295132, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁵⁸, 59058, F₃, 3, 21) (dual of [(59058, 3), 177016, 22]-NRT-code), using

OOA 3-folding [i] based on linear OA(3¹⁵⁸, 177174, F₃, 21) (dual of [177174, 177016, 22]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3¹⁵⁶, 177172, F₃, 21) (dual of [177172, 177016, 22]-code), using
  - constructionÂ X4 applied to C([0,10]) âŠ‚ C([0,9]) [i] based on
    1. 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]
    2. linear OA(3¹³³, 177148, F₃, 19) (dual of [177148, 177015, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148Â | 3²²âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
    3. linear OA(3²³, 24, F₃, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,3)), using
      - dual of repetition code with length 24 [i]
    4. linear OA(3¹, 24, F₃, 1) (dual of [24, 23, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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(3¹⁵⁹, 59058, F₃, 5, 21) (dual of [(59058, 5), 295131, 22]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3¹⁶⁰, 59058, F₃, 5, 21) (dual of [(59058, 5), 295130, 22]-NRT-code)	[i]		OOA Duplication