MinT - Information on Result #2766872

Information on Result #2766872

Linear OOA(2²³⁹, 66, F₂, 4, 142) (dual of [(66, 4), 25, 143]-NRT-code), using strength reduction based on linear OOA(2²³⁹, 66, F₂, 4, 143) (dual of [(66, 4), 25, 144]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹⁷, 22, F₃₂, 17) (dual of [22, 5, 18]-code or 22-arc in PG(16,32)), using
  - discarding factors / shortening the dual code based on linear OA(32¹⁷, 32, F₃₂, 17) (dual of [32, 15, 18]-code or 32-arc in PG(16,32)), using
    - Reedâ€“Solomon code RS(15,32) [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(2²⁴¹, 66, F₂, 4, 142) (dual of [(66, 4), 23, 143]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²³⁸, 65, F₂, 4, 141) (dual of [(65, 4), 22, 142]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(2²³⁷, 65, F₂, 4, 140) (dual of [(65, 4), 23, 141]-NRT-code)	[i]
4	Linear OOA(2²³⁶, 65, F₂, 4, 139) (dual of [(65, 4), 24, 140]-NRT-code)	[i]
5	Linear OOA(2²³⁵, 65, F₂, 4, 138) (dual of [(65, 4), 25, 139]-NRT-code)	[i]
6	Linear OOA(2²³⁴, 64, F₂, 4, 137) (dual of [(64, 4), 22, 138]-NRT-code)	[i]
7	Linear OOA(2²³³, 64, F₂, 4, 136) (dual of [(64, 4), 23, 137]-NRT-code)	[i]
8	Linear OOA(2²³², 64, F₂, 4, 135) (dual of [(64, 4), 24, 136]-NRT-code)	[i]
9	Linear OOA(2²³¹, 64, F₂, 4, 134) (dual of [(64, 4), 25, 135]-NRT-code)	[i]
10	Linear OOA(2²³⁰, 63, F₂, 4, 133) (dual of [(63, 4), 22, 134]-NRT-code)	[i]
11	Linear OOA(2²²⁹, 63, F₂, 4, 132) (dual of [(63, 4), 23, 133]-NRT-code)	[i]
12	Linear OOA(2²²⁶, 62, F₂, 4, 129) (dual of [(62, 4), 22, 130]-NRT-code)	[i]
13	Linear OOA(2²²⁵, 62, F₂, 4, 128) (dual of [(62, 4), 23, 129]-NRT-code)	[i]
14	Linear OOA(2²³⁹, 33, F₂, 8, 142) (dual of [(33, 8), 25, 143]-NRT-code)	[i]	OOA Folding