MinT - Information on Result #2766701

Information on Result #2766701

Linear OOA(2²³⁶, 69, F₂, 4, 125) (dual of [(69, 4), 40, 126]-NRT-code), using strength reduction based on linear OOA(2²³⁶, 69, F₂, 4, 127) (dual of [(69, 4), 40, 128]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹⁵, 23, F₃₂, 15) (dual of [23, 8, 16]-code or 23-arc in PG(14,32)), using
  - discarding factors / shortening the dual code based on linear OA(32¹⁵, 32, F₃₂, 15) (dual of [32, 17, 16]-code or 32-arc in PG(14,32)), using
    - Reedâ€“Solomon code RS(17,32) [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(2²³⁷, 69, F₂, 4, 125) (dual of [(69, 4), 39, 126]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²³⁵, 68, F₂, 4, 124) (dual of [(68, 4), 37, 125]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(2²³⁴, 68, F₂, 4, 123) (dual of [(68, 4), 38, 124]-NRT-code)	[i]
4	Linear OOA(2²³³, 68, F₂, 4, 122) (dual of [(68, 4), 39, 123]-NRT-code)	[i]
5	Linear OOA(2²³², 68, F₂, 4, 121) (dual of [(68, 4), 40, 122]-NRT-code)	[i]
6	Linear OOA(2²³¹, 67, F₂, 4, 120) (dual of [(67, 4), 37, 121]-NRT-code)	[i]
7	Linear OOA(2²³⁰, 67, F₂, 4, 119) (dual of [(67, 4), 38, 120]-NRT-code)	[i]
8	Linear OOA(2²²⁹, 67, F₂, 4, 118) (dual of [(67, 4), 39, 119]-NRT-code)	[i]
9	Linear OOA(2²²⁸, 67, F₂, 4, 117) (dual of [(67, 4), 40, 118]-NRT-code)	[i]
10	Linear OOA(2²²⁷, 66, F₂, 4, 116) (dual of [(66, 4), 37, 117]-NRT-code)	[i]
11	Linear OOA(2²²⁶, 66, F₂, 4, 115) (dual of [(66, 4), 38, 116]-NRT-code)	[i]
12	Linear OOA(2²²⁵, 66, F₂, 4, 114) (dual of [(66, 4), 39, 115]-NRT-code)	[i]
13	Linear OOA(2²²³, 65, F₂, 4, 112) (dual of [(65, 4), 37, 113]-NRT-code)	[i]