MinT - Information on Result #2234913

Information on Result #2234913

Linear OA(3²³⁷, 409, F₃, 78) (dual of [409, 172, 79]-code), using 1 times truncation based on linear OA(3²³⁸, 410, F₃, 79) (dual of [410, 172, 80]-code), using

concatenation of two codes [i] based on
1. linear OA(81³⁹, 82, F₈₁, 39) (dual of [82, 43, 40]-code or 82-arc in PG(38,81)), using
  - extended Reedâ€“Solomon code RS_e(43,81) [i]
  - the expurgated narrow-sense BCH-code C(I) with length 82Â | 81²âˆ’1, defining interval IÂ =Â [0,19], and minimum distance dÂ â‰¥ |{−19,−18,…,19}|+1Â =Â 40 (BCH-bound) [i]
2. linear OA(3¹, 5, F₃, 1) (dual of [5, 4, 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 OA(3²³⁹, 411, F₃, 78) (dual of [411, 172, 79]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(3²⁴⁰, 412, F₃, 78) (dual of [412, 172, 79]-code)	[i]
3	Linear OA(3²⁴¹, 413, F₃, 78) (dual of [413, 172, 79]-code)	[i]
4	Linear OA(3²⁴², 414, F₃, 78) (dual of [414, 172, 79]-code)	[i]
5	Linear OOA(3²³⁷, 204, F₃, 2, 78) (dual of [(204, 2), 171, 79]-NRT-code)	[i]	OOA Folding
6	Linear OOA(3²³⁷, 136, F₃, 3, 78) (dual of [(136, 3), 171, 79]-NRT-code)	[i]	OOA Folding