MinT - Information on Result #2486042

Information on Result #2486042

Linear OOA(3¹⁰⁴, 29537, F₃, 2, 15) (dual of [(29537, 2), 58970, 16]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3¹⁰², 29536, F₃, 2, 15) (dual of [(29536, 2), 58970, 16]-NRT-code), using

OOA 2-folding [i] based on linear OA(3¹⁰², 59072, F₃, 15) (dual of [59072, 58970, 16]-code), using
- constructionÂ X4 applied to C([0,7]) âŠ‚ C([0,6]) [i] based on
  1. linear OA(3¹⁰¹, 59050, F₃, 15) (dual of [59050, 58949, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 3²⁰âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
  2. linear OA(3⁸¹, 59050, F₃, 13) (dual of [59050, 58969, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 3²⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
  3. linear OA(3²¹, 22, F₃, 21) (dual of [22, 1, 22]-code or 22-arc in PG(20,3)), using
    - dual of repetition code with length 22 [i]
  4. linear OA(3¹, 22, F₃, 1) (dual of [22, 21, 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(3¹⁰⁵, 29537, F₃, 2, 15) (dual of [(29537, 2), 58969, 16]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3¹⁰⁴, 29537, F₃, 3, 15) (dual of [(29537, 3), 88507, 16]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(3¹⁰⁴, 29537, F₃, 4, 15) (dual of [(29537, 4), 118044, 16]-NRT-code)	[i]
4	Linear OOA(3¹⁰⁴, 29537, F₃, 5, 15) (dual of [(29537, 5), 147581, 16]-NRT-code)	[i]
5	Digital (89, 104, 29537)-net over F₃	[i]