MinT - Information on Result #2766534

Information on Result #2766534

Linear OOA(2²³⁴, 75, F₂, 4, 103) (dual of [(75, 4), 66, 104]-NRT-code), using strength reduction based on linear OOA(2²³⁴, 75, F₂, 4, 104) (dual of [(75, 4), 66, 105]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(64¹⁴, 25, F₆₄, 14) (dual of [25, 11, 15]-code or 25-arc in PG(13,64)), using
  - discarding factors / shortening the dual code based on linear OA(64¹⁴, 64, F₆₄, 14) (dual of [64, 50, 15]-code or 64-arc in PG(13,64)), using
    - Reedâ€“Solomon code RS(50,64) [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(2²³⁶, 75, F₂, 4, 103) (dual of [(75, 4), 64, 104]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²³⁷, 75, F₂, 4, 103) (dual of [(75, 4), 63, 104]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²³³, 74, F₂, 4, 102) (dual of [(74, 4), 63, 103]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(2²³², 74, F₂, 4, 101) (dual of [(74, 4), 64, 102]-NRT-code)	[i]
5	Linear OOA(2²³¹, 74, F₂, 4, 100) (dual of [(74, 4), 65, 101]-NRT-code)	[i]
6	Linear OOA(2²³⁰, 74, F₂, 4, 99) (dual of [(74, 4), 66, 100]-NRT-code)	[i]
7	Linear OOA(2²²⁹, 73, F₂, 4, 98) (dual of [(73, 4), 63, 99]-NRT-code)	[i]