MinT - Information on Result #639837

Information on Result #639837

Linear OA(8¹²³, 135, F₈, 87) (dual of [135, 12, 88]-code), using concatenation of two codes based on

linear OA(64²¹, 27, F₆₄, 21) (dual of [27, 6, 22]-code or 27-arc in PG(20,64)), using
- discarding factors / shortening the dual code based on linear OA(64²¹, 64, F₆₄, 21) (dual of [64, 43, 22]-code or 64-arc in PG(20,64)), using
  - Reedâ€“Solomon code RS(43,64) [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(8¹²³, 135, F₈, 86) (dual of [135, 12, 87]-code)	[i]		Strength Reduction
2	Linear OA(8¹²³, 135, F₈, 85) (dual of [135, 12, 86]-code)	[i]		Strength Reduction
3	Linear OA(8¹²², 134, F₈, 86) (dual of [134, 12, 87]-code)	[i]		Truncation
4	Linear OA(8¹²¹, 133, F₈, 85) (dual of [133, 12, 86]-code)	[i]
5	Linear OA(8¹²⁰, 132, F₈, 84) (dual of [132, 12, 85]-code)	[i]
6	Linear OA(8¹¹⁹, 131, F₈, 83) (dual of [131, 12, 84]-code)	[i]
7	Linear OA(8¹¹⁷, 129, F₈, 81) (dual of [129, 12, 82]-code)	[i]
8	Linear OA(8¹¹⁵, 127, F₈, 79) (dual of [127, 12, 80]-code)	[i]
9	Linear OA(8¹¹⁴, 126, F₈, 78) (dual of [126, 12, 79]-code)	[i]
10	Linear OOA(8¹²³, 67, F₈, 2, 87) (dual of [(67, 2), 11, 88]-NRT-code)	[i]		OOA Folding
11	Linear OOA(8¹²³, 45, F₈, 3, 87) (dual of [(45, 3), 12, 88]-NRT-code)	[i]		OOA Folding