MinT - Information on Result #2767010

Information on Result #2767010

Linear OOA(2²⁴¹, 69, F₂, 4, 133) (dual of [(69, 4), 35, 134]-NRT-code), using strength reduction based on linear OOA(2²⁴¹, 69, F₂, 4, 135) (dual of [(69, 4), 35, 136]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹⁶, 23, F₃₂, 16) (dual of [23, 7, 17]-code or 23-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(2²⁴², 69, F₂, 4, 133) (dual of [(69, 4), 34, 134]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²⁴⁰, 68, F₂, 4, 132) (dual of [(68, 4), 32, 133]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(2²³⁹, 68, F₂, 4, 131) (dual of [(68, 4), 33, 132]-NRT-code)	[i]
4	Linear OOA(2²³⁸, 68, F₂, 4, 130) (dual of [(68, 4), 34, 131]-NRT-code)	[i]
5	Linear OOA(2²³⁷, 68, F₂, 4, 129) (dual of [(68, 4), 35, 130]-NRT-code)	[i]
6	Linear OOA(2²³⁶, 67, F₂, 4, 128) (dual of [(67, 4), 32, 129]-NRT-code)	[i]
7	Linear OOA(2²³⁵, 67, F₂, 4, 127) (dual of [(67, 4), 33, 128]-NRT-code)	[i]
8	Linear OOA(2²³⁴, 67, F₂, 4, 126) (dual of [(67, 4), 34, 127]-NRT-code)	[i]
9	Linear OOA(2²³³, 67, F₂, 4, 125) (dual of [(67, 4), 35, 126]-NRT-code)	[i]
10	Linear OOA(2²³⁰, 66, F₂, 4, 122) (dual of [(66, 4), 34, 123]-NRT-code)	[i]
11	Linear OOA(2²²⁸, 65, F₂, 4, 120) (dual of [(65, 4), 32, 121]-NRT-code)	[i]