MinT - Information on Result #1088029

Information on Result #1088029

Linear OOA(2²¹⁶, 72, F₂, 4, 90) (dual of [(72, 4), 72, 91]-NRT-code), using concatenation of two NRT-codes based on

linear OA(64¹², 24, F₆₄, 12) (dual of [24, 12, 13]-code or 24-arc in PG(11,64)), using
- discarding factors / shortening the dual code based on linear OA(64¹², 64, F₆₄, 12) (dual of [64, 52, 13]-code or 64-arc in PG(11,64)), using
  - Reedâ€“Solomon code RS(52,64) [i]
linear OOA(2⁶, 3, F₂, 4, 6) (dual of [(3, 4), 6, 7]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(4;6,2) [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 OOA(2²¹⁶, 72, F₂, 4, 89) (dual of [(72, 4), 72, 90]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2²¹⁶, 72, F₂, 4, 88) (dual of [(72, 4), 72, 89]-NRT-code)	[i]
3	Linear OOA(2²¹⁶, 72, F₂, 4, 87) (dual of [(72, 4), 72, 88]-NRT-code)	[i]
4	Linear OOA(2²²⁰, 73, F₂, 4, 90) (dual of [(73, 4), 72, 91]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
5	Linear OOA(2²¹⁷, 72, F₂, 4, 90) (dual of [(72, 4), 71, 91]-NRT-code)	[i]		OOA Duplication
6	Linear OOA(2²¹⁸, 72, F₂, 4, 90) (dual of [(72, 4), 70, 91]-NRT-code)	[i]		OOA Duplication
7	Linear OOA(2²¹⁵, 71, F₂, 4, 89) (dual of [(71, 4), 69, 90]-NRT-code)	[i]		Truncation for OOAs
8	Linear OOA(2²¹⁴, 71, F₂, 4, 88) (dual of [(71, 4), 70, 89]-NRT-code)	[i]
9	Linear OOA(2²¹³, 71, F₂, 4, 87) (dual of [(71, 4), 71, 88]-NRT-code)	[i]
10	Linear OOA(2²¹⁶, 36, F₂, 7, 90) (dual of [(36, 7), 36, 91]-NRT-code)	[i]		OOA Folding
11	Linear OOA(2²¹⁶, 36, F₂, 8, 90) (dual of [(36, 8), 72, 91]-NRT-code)	[i]		OOA Folding