MinT - Information on Result #2764176

Information on Result #2764176

Linear OOA(2¹⁹⁸, 57, F₂, 4, 110) (dual of [(57, 4), 30, 111]-NRT-code), using strength reduction based on linear OOA(2¹⁹⁸, 57, F₂, 4, 111) (dual of [(57, 4), 30, 112]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹³, 19, F₃₂, 13) (dual of [19, 6, 14]-code or 19-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(2¹⁹⁹, 57, F₂, 4, 110) (dual of [(57, 4), 29, 111]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²⁰⁰, 57, F₂, 4, 110) (dual of [(57, 4), 28, 111]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2¹⁹⁷, 56, F₂, 4, 109) (dual of [(56, 4), 27, 110]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(2¹⁹⁶, 56, F₂, 4, 108) (dual of [(56, 4), 28, 109]-NRT-code)	[i]
5	Linear OOA(2¹⁹⁵, 56, F₂, 4, 107) (dual of [(56, 4), 29, 108]-NRT-code)	[i]
6	Linear OOA(2¹⁹⁴, 56, F₂, 4, 106) (dual of [(56, 4), 30, 107]-NRT-code)	[i]