MinT - Information on Result #2234468

Information on Result #2234468

Linear OA(3¹⁹³, 409, F₃, 56) (dual of [409, 216, 57]-code), using 1 times truncation based on linear OA(3¹⁹⁴, 410, F₃, 57) (dual of [410, 216, 58]-code), using

concatenation of two codes [i] based on
1. linear OA(81²⁸, 82, F₈₁, 28) (dual of [82, 54, 29]-code or 82-arc in PG(27,81)), using
  - extended Reedâ€“Solomon code RS_e(54,81) [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		This result only	Method
1	Linear OA(3¹⁹⁵, 411, F₃, 56) (dual of [411, 216, 57]-code)	[i]		Code Embedding in Larger Space
2	Linear OA(3¹⁹⁶, 412, F₃, 56) (dual of [412, 216, 57]-code)	[i]
3	Linear OA(3¹⁹⁷, 413, F₃, 56) (dual of [413, 216, 57]-code)	[i]
4	Linear OA(3¹⁹⁸, 414, F₃, 56) (dual of [414, 216, 57]-code)	[i]
5	Linear OOA(3¹⁹³, 204, F₃, 2, 56) (dual of [(204, 2), 215, 57]-NRT-code)	[i]		OOA Folding
6	Linear OOA(3¹⁹³, 136, F₃, 3, 56) (dual of [(136, 3), 215, 57]-NRT-code)	[i]		OOA Folding