MinT - Information on Result #812779

Information on Result #812779

Linear OOA(3⁶³, 29531, F₃, 2, 10) (dual of [(29531, 2), 58999, 11]-NRT-code), using OOA 2-folding based on linear OA(3⁶³, 59062, F₃, 10) (dual of [59062, 58999, 11]-code), using

1 times code embedding in larger space [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		Method
1	Linear OOA(3⁶⁴, 29531, F₃, 2, 10) (dual of [(29531, 2), 58998, 11]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3⁶³, 24297, F₃, 3, 10) (dual of [(24297, 3), 72828, 11]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(3⁶³, 24297, F₃, 4, 10) (dual of [(24297, 4), 97125, 11]-NRT-code)	[i]
4	Linear OOA(3⁶³, 24297, F₃, 5, 10) (dual of [(24297, 5), 121422, 11]-NRT-code)	[i]
5	Digital (53, 63, 24297)-net over F₃	[i]