MinT - Information on Result #2766530

Information on Result #2766530

Linear OOA(2²³⁴, 66, F₂, 4, 133) (dual of [(66, 4), 30, 134]-NRT-code), using strength reduction based on linear OOA(2²³⁴, 66, F₂, 4, 135) (dual of [(66, 4), 30, 136]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹⁶, 22, F₃₂, 16) (dual of [22, 6, 17]-code or 22-arc in PG(15,32)), using
  - discarding factors / shortening the dual code based on linear OA(32¹⁶, 32, F₃₂, 16) (dual of [32, 16, 17]-code or 32-arc in PG(15,32)), using
    - Reedâ€“Solomon code RS(16,32) [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(2²³⁵, 66, F₂, 4, 133) (dual of [(66, 4), 29, 134]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²³³, 65, F₂, 4, 132) (dual of [(65, 4), 27, 133]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(2²³², 65, F₂, 4, 131) (dual of [(65, 4), 28, 132]-NRT-code)	[i]
4	Linear OOA(2²³¹, 65, F₂, 4, 130) (dual of [(65, 4), 29, 131]-NRT-code)	[i]
5	Linear OOA(2²³⁰, 65, F₂, 4, 129) (dual of [(65, 4), 30, 130]-NRT-code)	[i]
6	Linear OOA(2²²⁹, 64, F₂, 4, 128) (dual of [(64, 4), 27, 129]-NRT-code)	[i]
7	Linear OOA(2²²⁸, 64, F₂, 4, 127) (dual of [(64, 4), 28, 128]-NRT-code)	[i]
8	Linear OOA(2²²⁷, 64, F₂, 4, 126) (dual of [(64, 4), 29, 127]-NRT-code)	[i]
9	Linear OOA(2²²⁶, 64, F₂, 4, 125) (dual of [(64, 4), 30, 126]-NRT-code)	[i]
10	Linear OOA(2²²⁵, 63, F₂, 4, 124) (dual of [(63, 4), 27, 125]-NRT-code)	[i]
11	Linear OOA(2²²³, 63, F₂, 4, 122) (dual of [(63, 4), 29, 123]-NRT-code)	[i]
12	Linear OOA(2²²¹, 62, F₂, 4, 120) (dual of [(62, 4), 27, 121]-NRT-code)	[i]
13	Linear OOA(2²³⁴, 33, F₂, 8, 133) (dual of [(33, 8), 30, 134]-NRT-code)	[i]	OOA Folding