MinT - Information on Result #2765584

Information on Result #2765584

Linear OOA(2²¹⁹, 66, F₂, 4, 110) (dual of [(66, 4), 45, 111]-NRT-code), using strength reduction based on linear OOA(2²¹⁹, 66, F₂, 4, 111) (dual of [(66, 4), 45, 112]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹³, 22, F₃₂, 13) (dual of [22, 9, 14]-code or 22-arc in PG(12,32)), using
  - discarding factors / shortening the dual code based on linear OA(32¹³, 32, F₃₂, 13) (dual of [32, 19, 14]-code or 32-arc in PG(12,32)), using
    - Reedâ€“Solomon code RS(19,32) [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(2²²⁰, 66, F₂, 4, 110) (dual of [(66, 4), 44, 111]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²²¹, 66, F₂, 4, 110) (dual of [(66, 4), 43, 111]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²¹⁸, 65, F₂, 4, 109) (dual of [(65, 4), 42, 110]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(2²¹⁷, 65, F₂, 4, 108) (dual of [(65, 4), 43, 109]-NRT-code)	[i]
5	Linear OOA(2²¹⁶, 65, F₂, 4, 107) (dual of [(65, 4), 44, 108]-NRT-code)	[i]
6	Linear OOA(2²¹⁵, 65, F₂, 4, 106) (dual of [(65, 4), 45, 107]-NRT-code)	[i]
7	Linear OOA(2²¹⁴, 64, F₂, 4, 105) (dual of [(64, 4), 42, 106]-NRT-code)	[i]
8	Linear OOA(2²¹³, 64, F₂, 4, 104) (dual of [(64, 4), 43, 105]-NRT-code)	[i]
9	Linear OOA(2²¹², 64, F₂, 4, 103) (dual of [(64, 4), 44, 104]-NRT-code)	[i]
10	Linear OOA(2²¹¹, 64, F₂, 4, 102) (dual of [(64, 4), 45, 103]-NRT-code)	[i]
11	Linear OOA(2²¹⁹, 33, F₂, 7, 110) (dual of [(33, 7), 12, 111]-NRT-code)	[i]	OOA Folding
12	Linear OOA(2²¹⁹, 33, F₂, 8, 110) (dual of [(33, 8), 45, 111]-NRT-code)	[i]	OOA Folding