MinT - Information on Result #2767321

Information on Result #2767321

Linear OOA(2²⁴⁶, 78, F₂, 4, 110) (dual of [(78, 4), 66, 111]-NRT-code), using strength reduction based on linear OOA(2²⁴⁶, 78, F₂, 4, 111) (dual of [(78, 4), 66, 112]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(64¹⁵, 26, F₆₄, 15) (dual of [26, 11, 16]-code or 26-arc in PG(14,64)), using
  - discarding factors / shortening the dual code based on linear OA(64¹⁵, 64, F₆₄, 15) (dual of [64, 49, 16]-code or 64-arc in PG(14,64)), using
    - Reedâ€“Solomon code RS(49,64) [i]
2. linear OOA(2⁶, 3, F₂, 4, 6) (dual of [(3, 4), 6, 7]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(4;6,2) [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(2²⁴⁸, 78, F₂, 4, 110) (dual of [(78, 4), 64, 111]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²⁴⁹, 78, F₂, 4, 110) (dual of [(78, 4), 63, 111]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁴⁵, 77, F₂, 4, 109) (dual of [(77, 4), 63, 110]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(2²⁴⁴, 77, F₂, 4, 108) (dual of [(77, 4), 64, 109]-NRT-code)	[i]
5	Linear OOA(2²⁴³, 77, F₂, 4, 107) (dual of [(77, 4), 65, 108]-NRT-code)	[i]
6	Linear OOA(2²⁴², 77, F₂, 4, 106) (dual of [(77, 4), 66, 107]-NRT-code)	[i]
7	Linear OOA(2²⁴¹, 76, F₂, 4, 105) (dual of [(76, 4), 63, 106]-NRT-code)	[i]
8	Linear OOA(2²⁴⁶, 39, F₂, 7, 110) (dual of [(39, 7), 27, 111]-NRT-code)	[i]	OOA Folding
9	Linear OOA(2²⁴⁶, 39, F₂, 8, 110) (dual of [(39, 8), 66, 111]-NRT-code)	[i]	OOA Folding