MinT - Information on Result #2766109

Information on Result #2766109

Linear OOA(2²²⁷, 63, F₂, 4, 133) (dual of [(63, 4), 25, 134]-NRT-code), using strength reduction based on linear OOA(2²²⁷, 63, F₂, 4, 135) (dual of [(63, 4), 25, 136]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹⁶, 21, F₃₂, 16) (dual of [21, 5, 17]-code or 21-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(2²²⁶, 62, F₂, 4, 132) (dual of [(62, 4), 22, 133]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(2²²⁵, 62, F₂, 4, 131) (dual of [(62, 4), 23, 132]-NRT-code)	[i]
3	Linear OOA(2²²⁴, 62, F₂, 4, 130) (dual of [(62, 4), 24, 131]-NRT-code)	[i]
4	Linear OOA(2²²³, 62, F₂, 4, 129) (dual of [(62, 4), 25, 130]-NRT-code)	[i]
5	Linear OOA(2²²², 61, F₂, 4, 128) (dual of [(61, 4), 22, 129]-NRT-code)	[i]
6	Linear OOA(2²²¹, 61, F₂, 4, 127) (dual of [(61, 4), 23, 128]-NRT-code)	[i]
7	Linear OOA(2²²⁰, 61, F₂, 4, 126) (dual of [(61, 4), 24, 127]-NRT-code)	[i]
8	Linear OOA(2²¹⁹, 61, F₂, 4, 125) (dual of [(61, 4), 25, 126]-NRT-code)	[i]
9	Linear OOA(2²¹⁸, 60, F₂, 4, 124) (dual of [(60, 4), 22, 125]-NRT-code)	[i]
10	Linear OOA(2²¹⁷, 60, F₂, 4, 123) (dual of [(60, 4), 23, 124]-NRT-code)	[i]
11	Linear OOA(2²¹⁴, 59, F₂, 4, 120) (dual of [(59, 4), 22, 121]-NRT-code)	[i]