MinT - Information on Result #1087956

Information on Result #1087956

Linear OOA(2²²⁸, 72, F₂, 4, 103) (dual of [(72, 4), 60, 104]-NRT-code), using concatenation of two NRT-codes based on

linear OA(32¹², 24, F₃₂, 12) (dual of [24, 12, 13]-code or 24-arc in PG(11,32)), using
- discarding factors / shortening the dual code based on linear OA(32¹², 32, F₃₂, 12) (dual of [32, 20, 13]-code or 32-arc in PG(11,32)), using
  - Reedâ€“Solomon code RS(20,32) [i]
linear OOA(2⁷, 3, F₂, 4, 7) (dual of [(3, 4), 5, 8]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(4;5,2) [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(2²²⁸, 72, F₂, 4, 102) (dual of [(72, 4), 60, 103]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2²²⁸, 72, F₂, 4, 101) (dual of [(72, 4), 60, 102]-NRT-code)	[i]
3	Linear OOA(2²²⁸, 72, F₂, 4, 100) (dual of [(72, 4), 60, 101]-NRT-code)	[i]
4	Linear OOA(2²²⁸, 72, F₂, 4, 99) (dual of [(72, 4), 60, 100]-NRT-code)	[i]
5	Linear OOA(2²²⁹, 72, F₂, 4, 103) (dual of [(72, 4), 59, 104]-NRT-code)	[i]		OOA Duplication
6	Linear OOA(2²³⁰, 72, F₂, 4, 103) (dual of [(72, 4), 58, 104]-NRT-code)	[i]		OOA Duplication
7	Linear OOA(2²²⁷, 71, F₂, 4, 102) (dual of [(71, 4), 57, 103]-NRT-code)	[i]		Truncation for OOAs
8	Linear OOA(2²²⁶, 71, F₂, 4, 101) (dual of [(71, 4), 58, 102]-NRT-code)	[i]
9	Linear OOA(2²²⁵, 71, F₂, 4, 100) (dual of [(71, 4), 59, 101]-NRT-code)	[i]
10	Linear OOA(2²²⁴, 71, F₂, 4, 99) (dual of [(71, 4), 60, 100]-NRT-code)	[i]
11	Linear OOA(2²²³, 70, F₂, 4, 98) (dual of [(70, 4), 57, 99]-NRT-code)	[i]
12	Linear OOA(2²²⁸, 36, F₂, 7, 103) (dual of [(36, 7), 24, 104]-NRT-code)	[i]		OOA Folding
13	Linear OOA(2²²⁸, 36, F₂, 8, 103) (dual of [(36, 8), 60, 104]-NRT-code)	[i]		OOA Folding