MinT - Information on Result #2192486

Information on Result #2192486

Linear OA(3¹³², 144, F₃, 76) (dual of [144, 12, 77]-code), using strength reduction based on linear OA(3¹³², 144, F₃, 77) (dual of [144, 12, 78]-code), using

concatenation of two codes [i] based on
1. linear OA(27¹², 16, F₂₇, 12) (dual of [16, 4, 13]-code or 16-arc in PG(11,27)), using
  - discarding factors / shortening the dual code based on linear OA(27¹², 27, F₂₇, 12) (dual of [27, 15, 13]-code or 27-arc in PG(11,27)), using
    - Reedâ€“Solomon code RS(15,27) [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(3¹³¹, 143, F₃, 75) (dual of [143, 12, 76]-code)	[i]	Truncation
2	Linear OA(3¹³⁰, 142, F₃, 74) (dual of [142, 12, 75]-code)	[i]
3	Linear OA(3¹²⁹, 141, F₃, 73) (dual of [141, 12, 74]-code)	[i]
4	Linear OOA(3¹³², 72, F₃, 2, 76) (dual of [(72, 2), 12, 77]-NRT-code)	[i]	OOA Folding
5	Linear OOA(3¹³², 48, F₃, 3, 76) (dual of [(48, 3), 12, 77]-NRT-code)	[i]	OOA Folding