MinT - Information on Result #640727

Information on Result #640727

Linear OA(9¹³⁸, 150, F₉, 99) (dual of [150, 12, 100]-code), using concatenation of two codes based on

linear OA(81²⁴, 30, F₈₁, 24) (dual of [30, 6, 25]-code or 30-arc in PG(23,81)), using
- discarding factors / shortening the dual code based on linear OA(81²⁴, 81, F₈₁, 24) (dual of [81, 57, 25]-code or 81-arc in PG(23,81)), using
  - Reedâ€“Solomon code RS(57,81) [i]
linear OA(9³, 5, F₉, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,9) or 5-cap in PG(2,9)), using
- discarding factors / shortening the dual code based on linear OA(9³, 9, F₉, 3) (dual of [9, 6, 4]-code or 9-arc in PG(2,9) or 9-cap in PG(2,9)), using
  - Reedâ€“Solomon code RS(6,9) [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(9¹³⁸, 150, F₉, 98) (dual of [150, 12, 99]-code)	[i]		Strength Reduction
2	Linear OA(9¹³⁷, 149, F₉, 98) (dual of [149, 12, 99]-code)	[i]		Truncation
3	Linear OA(9¹³⁶, 148, F₉, 97) (dual of [148, 12, 98]-code)	[i]
4	Linear OA(9¹³⁵, 147, F₉, 96) (dual of [147, 12, 97]-code)	[i]
5	Linear OA(9¹³⁴, 146, F₉, 95) (dual of [146, 12, 96]-code)	[i]
6	Linear OA(9¹³¹, 143, F₉, 92) (dual of [143, 12, 93]-code)	[i]
7	Linear OA(9¹³⁰, 142, F₉, 91) (dual of [142, 12, 92]-code)	[i]
8	Linear OA(9¹²⁹, 141, F₉, 90) (dual of [141, 12, 91]-code)	[i]
9	Linear OA(9¹²⁷, 139, F₉, 88) (dual of [139, 12, 89]-code)	[i]
10	Linear OOA(9¹³⁸, 75, F₉, 2, 99) (dual of [(75, 2), 12, 100]-NRT-code)	[i]		OOA Folding
11	Linear OOA(9¹³⁸, 50, F₉, 3, 99) (dual of [(50, 3), 12, 100]-NRT-code)	[i]		OOA Folding