MinT - Information on Result #639862

Information on Result #639862

Linear OA(8¹⁵¹, 165, F₈, 107) (dual of [165, 14, 108]-code), using concatenation of two codes based on

linear OA(64²⁶, 33, F₆₄, 26) (dual of [33, 7, 27]-code or 33-arc in PG(25,64)), using
- discarding factors / shortening the dual code based on linear OA(64²⁶, 64, F₆₄, 26) (dual of [64, 38, 27]-code or 64-arc in PG(25,64)), using
  - Reedâ€“Solomon code RS(38,64) [i]
linear OA(8³, 5, F₈, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,8) or 5-cap in PG(2,8)), using
- discarding factors / shortening the dual code based on linear OA(8³, 8, F₈, 3) (dual of [8, 5, 4]-code or 8-arc in PG(2,8) or 8-cap in PG(2,8)), using
  - Reedâ€“Solomon code RS(5,8) [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(8¹⁵¹, 165, F₈, 106) (dual of [165, 14, 107]-code)	[i]		Strength Reduction
2	Linear OA(8¹⁵¹, 165, F₈, 105) (dual of [165, 14, 106]-code)	[i]		Strength Reduction
3	Linear OA(8¹⁵⁰, 164, F₈, 106) (dual of [164, 14, 107]-code)	[i]		Truncation
4	Linear OA(8¹⁴⁹, 163, F₈, 105) (dual of [163, 14, 106]-code)	[i]
5	Linear OA(8¹⁴⁸, 162, F₈, 104) (dual of [162, 14, 105]-code)	[i]
6	Linear OA(8¹⁴⁷, 161, F₈, 103) (dual of [161, 14, 104]-code)	[i]
7	Linear OA(8¹⁴⁵, 159, F₈, 101) (dual of [159, 14, 102]-code)	[i]
8	Linear OA(8¹⁴⁴, 158, F₈, 100) (dual of [158, 14, 101]-code)	[i]
9	Linear OA(8¹⁴³, 157, F₈, 99) (dual of [157, 14, 100]-code)	[i]
10	Linear OA(8¹⁴⁰, 154, F₈, 96) (dual of [154, 14, 97]-code)	[i]
11	Linear OOA(8¹⁵¹, 82, F₈, 2, 107) (dual of [(82, 2), 13, 108]-NRT-code)	[i]		OOA Folding
12	Linear OOA(8¹⁵¹, 55, F₈, 3, 107) (dual of [(55, 3), 14, 108]-NRT-code)	[i]		OOA Folding