MinT - Information on Result #2768100

Information on Result #2768100

Linear OOA(2²⁵⁷, 78, F₂, 4, 124) (dual of [(78, 4), 55, 125]-NRT-code), using strength reduction based on linear OOA(2²⁵⁷, 78, F₂, 4, 127) (dual of [(78, 4), 55, 128]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹⁵, 26, F₃₂, 15) (dual of [26, 11, 16]-code or 26-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(2²⁵⁸, 78, F₂, 4, 124) (dual of [(78, 4), 54, 125]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²⁵⁹, 78, F₂, 4, 124) (dual of [(78, 4), 53, 125]-NRT-code)	[i]
3	Linear OOA(2²⁶⁰, 78, F₂, 4, 124) (dual of [(78, 4), 52, 125]-NRT-code)	[i]
4	Linear OOA(2²⁵⁶, 77, F₂, 4, 123) (dual of [(77, 4), 52, 124]-NRT-code)	[i]	Truncation for OOAs
5	Linear OOA(2²⁵⁵, 77, F₂, 4, 122) (dual of [(77, 4), 53, 123]-NRT-code)	[i]
6	Linear OOA(2²⁵⁴, 77, F₂, 4, 121) (dual of [(77, 4), 54, 122]-NRT-code)	[i]
7	Linear OOA(2²⁵³, 77, F₂, 4, 120) (dual of [(77, 4), 55, 121]-NRT-code)	[i]
8	Linear OOA(2²⁵⁷, 39, F₂, 7, 124) (dual of [(39, 7), 16, 125]-NRT-code)	[i]	OOA Folding
9	Linear OOA(2²⁵⁷, 39, F₂, 8, 124) (dual of [(39, 8), 55, 125]-NRT-code)	[i]	OOA Folding