MinT - Information on Result #2194180

Information on Result #2194180

Linear OA(3¹⁶⁸, 189, F₃, 87) (dual of [189, 21, 88]-code), using strength reduction based on linear OA(3¹⁶⁸, 189, F₃, 89) (dual of [189, 21, 90]-code), using

concatenation of two codes [i] based on
1. linear OA(27¹⁴, 21, F₂₇, 14) (dual of [21, 7, 15]-code or 21-arc in PG(13,27)), using
  - discarding factors / shortening the dual code based on linear OA(27¹⁴, 27, F₂₇, 14) (dual of [27, 13, 15]-code or 27-arc in PG(13,27)), using
    - Reedâ€“Solomon code RS(13,27) [i]
2. linear OA(3⁶, 9, F₃, 5) (dual of [9, 3, 6]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁶, 10, F₃, 5) (dual of [10, 4, 6]-code), using
    - projective code from ovoid in PG(3,Â 3) [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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OA(3¹⁶⁷, 188, F₃, 86) (dual of [188, 21, 87]-code)	[i]	Truncation
2	Linear OA(3¹⁶⁶, 187, F₃, 85) (dual of [187, 21, 86]-code)	[i]
3	Linear OA(3¹⁶⁵, 186, F₃, 84) (dual of [186, 21, 85]-code)	[i]
4	Linear OA(3¹⁶⁴, 185, F₃, 83) (dual of [185, 21, 84]-code)	[i]
5	Linear OA(3¹⁶², 183, F₃, 81) (dual of [183, 21, 82]-code)	[i]
6	Linear OA(3¹⁶¹, 182, F₃, 80) (dual of [182, 21, 81]-code)	[i]
7	Linear OOA(3¹⁶⁸, 63, F₃, 3, 87) (dual of [(63, 3), 21, 88]-NRT-code)	[i]	OOA Folding