MinT - Information on Result #1094835

Information on Result #1094835

Linear OOA(3⁶¹, 14764, F₃, 5, 9) (dual of [(14764, 5), 73759, 10]-NRT-code), using OOA 4-folding and stacking with additional row based on linear OA(3⁶¹, 59057, F₃, 9) (dual of [59057, 58996, 10]-code), using

discarding factors / shortening the dual code based on linear OA(3⁶¹, 59060, F₃, 9) (dual of [59060, 58999, 10]-code), using
- 1 times truncation [i] based on linear OA(3⁶², 59061, F₃, 10) (dual of [59061, 58999, 11]-code), using
  - constructionÂ X4 applied to C_e(9) âŠ‚ C_e(7) [i] based on
    1. linear OA(3⁶¹, 59049, F₃, 10) (dual of [59049, 58988, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
    2. linear OA(3⁵¹, 59049, F₃, 8) (dual of [59049, 58998, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
    3. linear OA(3¹¹, 12, F₃, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,3)), using
      - dual of repetition code with length 12 [i]
    4. linear OA(3¹, 12, F₃, 1) (dual of [12, 11, 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: Constructive and 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(3²⁴¹, 1692484, F₃, 5, 18) (dual of [(1692484, 5), 8462179, 19]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(3²⁴², 1692484, F₃, 5, 19) (dual of [(1692484, 5), 8462178, 20]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs