MinT - Information on Result #2765254

Information on Result #2765254

Linear OOA(2²¹⁴, 66, F₂, 4, 101) (dual of [(66, 4), 50, 102]-NRT-code), using strength reduction based on linear OOA(2²¹⁴, 66, F₂, 4, 103) (dual of [(66, 4), 50, 104]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹², 22, F₃₂, 12) (dual of [22, 10, 13]-code or 22-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]
2. 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		Method
1	Linear OOA(2²¹⁵, 66, F₂, 4, 101) (dual of [(66, 4), 49, 102]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²¹³, 65, F₂, 4, 100) (dual of [(65, 4), 47, 101]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(2²¹², 65, F₂, 4, 99) (dual of [(65, 4), 48, 100]-NRT-code)	[i]
4	Linear OOA(2²¹¹, 65, F₂, 4, 98) (dual of [(65, 4), 49, 99]-NRT-code)	[i]
5	Linear OOA(2²¹⁴, 33, F₂, 7, 101) (dual of [(33, 7), 17, 102]-NRT-code)	[i]	OOA Folding
6	Linear OOA(2²¹⁴, 33, F₂, 8, 101) (dual of [(33, 8), 50, 102]-NRT-code)	[i]	OOA Folding