MinT - Information on Result #2767820

Information on Result #2767820

Linear OOA(2²⁵³, 72, F₂, 4, 139) (dual of [(72, 4), 35, 140]-NRT-code), using strength reduction based on linear OOA(2²⁵³, 72, F₂, 4, 143) (dual of [(72, 4), 35, 144]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹⁷, 24, F₃₂, 17) (dual of [24, 7, 18]-code or 24-arc in PG(16,32)), using
  - discarding factors / shortening the dual code based on linear OA(32¹⁷, 32, F₃₂, 17) (dual of [32, 15, 18]-code or 32-arc in PG(16,32)), using
    - Reedâ€“Solomon code RS(15,32) [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(2²⁵⁴, 72, F₂, 4, 139) (dual of [(72, 4), 34, 140]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²⁵⁵, 72, F₂, 4, 139) (dual of [(72, 4), 33, 140]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁵², 71, F₂, 4, 138) (dual of [(71, 4), 32, 139]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(2²⁵¹, 71, F₂, 4, 137) (dual of [(71, 4), 33, 138]-NRT-code)	[i]
5	Linear OOA(2²⁵⁰, 71, F₂, 4, 136) (dual of [(71, 4), 34, 137]-NRT-code)	[i]
6	Linear OOA(2²⁵³, 36, F₂, 8, 139) (dual of [(36, 8), 35, 140]-NRT-code)	[i]	OOA Folding