MinT - Information on Result #2767137

Information on Result #2767137

Linear OOA(2²⁴³, 72, F₂, 4, 124) (dual of [(72, 4), 45, 125]-NRT-code), using strength reduction based on linear OOA(2²⁴³, 72, F₂, 4, 127) (dual of [(72, 4), 45, 128]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹⁵, 24, F₃₂, 15) (dual of [24, 9, 16]-code or 24-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(2²⁴², 71, F₂, 4, 123) (dual of [(71, 4), 42, 124]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(2²⁴¹, 71, F₂, 4, 122) (dual of [(71, 4), 43, 123]-NRT-code)	[i]
3	Linear OOA(2²⁴⁰, 71, F₂, 4, 121) (dual of [(71, 4), 44, 122]-NRT-code)	[i]
4	Linear OOA(2²³⁹, 71, F₂, 4, 120) (dual of [(71, 4), 45, 121]-NRT-code)	[i]
5	Linear OOA(2²⁴³, 36, F₂, 7, 124) (dual of [(36, 7), 9, 125]-NRT-code)	[i]	OOA Folding
6	Linear OOA(2²⁴³, 36, F₂, 8, 124) (dual of [(36, 8), 45, 125]-NRT-code)	[i]	OOA Folding