MinT - Information on Result #2197297

Information on Result #2197297

Linear OA(3²¹⁹, 234, F₃, 130) (dual of [234, 15, 131]-code), using strength reduction based on linear OA(3²¹⁹, 234, F₃, 131) (dual of [234, 15, 132]-code), using

concatenation of two codes [i] based on
1. linear OA(27²¹, 26, F₂₇, 21) (dual of [26, 5, 22]-code or 26-arc in PG(20,27)), using
  - discarding factors / shortening the dual code based on linear OA(27²¹, 27, F₂₇, 21) (dual of [27, 6, 22]-code or 27-arc in PG(20,27)), using
    - Reedâ€“Solomon code RS(6,27) [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(3²¹⁸, 233, F₃, 129) (dual of [233, 15, 130]-code)	[i]	Truncation
2	Linear OA(3²¹⁷, 232, F₃, 128) (dual of [232, 15, 129]-code)	[i]
3	Linear OA(3²¹⁶, 231, F₃, 127) (dual of [231, 15, 128]-code)	[i]
4	Linear OA(3²¹⁵, 230, F₃, 126) (dual of [230, 15, 127]-code)	[i]
5	Linear OA(3²¹⁴, 229, F₃, 125) (dual of [229, 15, 126]-code)	[i]
6	Linear OA(3²¹³, 228, F₃, 124) (dual of [228, 15, 125]-code)	[i]
7	Linear OA(3²¹², 227, F₃, 123) (dual of [227, 15, 124]-code)	[i]
8	Linear OA(3²¹¹, 226, F₃, 122) (dual of [226, 15, 123]-code)	[i]
9	Linear OA(3²⁰⁹, 224, F₃, 120) (dual of [224, 15, 121]-code)	[i]
10	Linear OOA(3²¹⁹, 117, F₃, 2, 130) (dual of [(117, 2), 15, 131]-NRT-code)	[i]	OOA Folding
11	Linear OOA(3²¹⁹, 78, F₃, 3, 130) (dual of [(78, 3), 15, 131]-NRT-code)	[i]	OOA Folding