MinT - Information on Result #2765911

Information on Result #2765911

Linear OOA(2²²⁴, 66, F₂, 4, 117) (dual of [(66, 4), 40, 118]-NRT-code), using strength reduction based on linear OOA(2²²⁴, 66, F₂, 4, 119) (dual of [(66, 4), 40, 120]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹⁴, 22, F₃₂, 14) (dual of [22, 8, 15]-code or 22-arc in PG(13,32)), using
  - discarding factors / shortening the dual code based on linear OA(32¹⁴, 32, F₃₂, 14) (dual of [32, 18, 15]-code or 32-arc in PG(13,32)), using
    - Reedâ€“Solomon code RS(18,32) [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(2²²⁵, 66, F₂, 4, 117) (dual of [(66, 4), 39, 118]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²²³, 65, F₂, 4, 116) (dual of [(65, 4), 37, 117]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(2²²², 65, F₂, 4, 115) (dual of [(65, 4), 38, 116]-NRT-code)	[i]
4	Linear OOA(2²²¹, 65, F₂, 4, 114) (dual of [(65, 4), 39, 115]-NRT-code)	[i]
5	Linear OOA(2²²⁰, 65, F₂, 4, 113) (dual of [(65, 4), 40, 114]-NRT-code)	[i]
6	Linear OOA(2²¹⁹, 64, F₂, 4, 112) (dual of [(64, 4), 37, 113]-NRT-code)	[i]
7	Linear OOA(2²¹⁸, 64, F₂, 4, 111) (dual of [(64, 4), 38, 112]-NRT-code)	[i]
8	Linear OOA(2²¹⁷, 64, F₂, 4, 110) (dual of [(64, 4), 39, 111]-NRT-code)	[i]
9	Linear OOA(2²¹⁶, 64, F₂, 4, 109) (dual of [(64, 4), 40, 110]-NRT-code)	[i]
10	Linear OOA(2²¹⁵, 63, F₂, 4, 108) (dual of [(63, 4), 37, 109]-NRT-code)	[i]
11	Linear OOA(2²¹⁴, 63, F₂, 4, 107) (dual of [(63, 4), 38, 108]-NRT-code)	[i]
12	Linear OOA(2²¹³, 63, F₂, 4, 106) (dual of [(63, 4), 39, 107]-NRT-code)	[i]
13	Linear OOA(2²²⁴, 33, F₂, 7, 117) (dual of [(33, 7), 7, 118]-NRT-code)	[i]	OOA Folding
14	Linear OOA(2²²⁴, 33, F₂, 8, 117) (dual of [(33, 8), 40, 118]-NRT-code)	[i]	OOA Folding