MinT - Information on Result #812850

Information on Result #812850

Linear OOA(3⁷³, 29531, F₃, 2, 11) (dual of [(29531, 2), 58989, 12]-NRT-code), using OOA 2-folding based on linear OA(3⁷³, 59062, F₃, 11) (dual of [59062, 58989, 12]-code), using

1 times code embedding in larger space [i] based on linear OA(3⁷², 59061, F₃, 11) (dual of [59061, 58989, 12]-code), using
- constructionÂ X4 applied to C([0,10]) âŠ‚ C([1,9]) [i] based on
  1. linear OA(3⁷¹, 59048, F₃, 11) (dual of [59048, 58977, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [0,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
  2. linear OA(3⁶⁰, 59048, F₃, 9) (dual of [59048, 58988, 10]-code), using 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]
  3. linear OA(3¹², 13, F₃, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,3)), using
    - dual of repetition code with length 13 [i]
  4. linear OA(3¹, 13, F₃, 1) (dual of [13, 12, 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(3⁷⁴, 29531, F₃, 2, 11) (dual of [(29531, 2), 58988, 12]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3⁷³, 29531, F₃, 3, 11) (dual of [(29531, 3), 88520, 12]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(3⁷³, 29531, F₃, 4, 11) (dual of [(29531, 4), 118051, 12]-NRT-code)	[i]
4	Linear OOA(3⁷³, 29531, F₃, 5, 11) (dual of [(29531, 5), 147582, 12]-NRT-code)	[i]
5	Digital (62, 73, 29531)-net over F₃	[i]