MinT - Information on Result #2485250

Information on Result #2485250

Linear OOA(3⁷⁰, 88587, F₃, 2, 9) (dual of [(88587, 2), 177104, 10]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3⁶⁸, 88586, F₃, 2, 9) (dual of [(88586, 2), 177104, 10]-NRT-code), using

OOA 2-folding [i] based on linear OA(3⁶⁸, 177172, F₃, 9) (dual of [177172, 177104, 10]-code), using
- constructionÂ X4 applied to C([0,4]) âŠ‚ C([0,3]) [i] based on
  1. linear OA(3⁶⁷, 177148, F₃, 9) (dual of [177148, 177081, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148Â | 3²²âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
  2. linear OA(3⁴⁵, 177148, F₃, 7) (dual of [177148, 177103, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148Â | 3²²âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (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: 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(3⁷¹, 88587, F₃, 2, 9) (dual of [(88587, 2), 177103, 10]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3⁷⁰, 88587, F₃, 3, 9) (dual of [(88587, 3), 265691, 10]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(3⁷⁰, 88587, F₃, 4, 9) (dual of [(88587, 4), 354278, 10]-NRT-code)	[i]
4	Linear OOA(3⁷⁰, 88587, F₃, 5, 9) (dual of [(88587, 5), 442865, 10]-NRT-code)	[i]
5	Digital (61, 70, 88587)-net over F₃	[i]