MinT - Information on Result #2416607

Information on Result #2416607

Linear OOA(2²⁴, 15, F₂, 2, 14) (dual of [(15, 2), 6, 15]-NRT-code), using strength reduction based on linear OOA(2²⁴, 15, F₂, 2, 15) (dual of [(15, 2), 6, 16]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(8³, 5, F₈, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,8) or 5-cap in PG(2,8)), using
  - discarding factors / shortening the dual code based on linear OA(8³, 8, F₈, 3) (dual of [8, 5, 4]-code or 8-arc in PG(2,8) or 8-cap in PG(2,8)), using
    - Reedâ€“Solomon code RS(5,8) [i]
2. linear OOA(2³, 3, F₂, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(2;3,2) [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(2⁵³, 30, F₂, 2, 28) (dual of [(30, 2), 7, 29]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(2⁵³, 30, F₂, 2, 29) (dual of [(30, 2), 7, 30]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(2¹²⁶, 66, F₂, 2, 68) (dual of [(66, 2), 6, 69]-NRT-code)	[i]	Juxtaposition for OOAs
4	Linear OOA(2¹⁶⁰, 83, F₂, 2, 86) (dual of [(83, 2), 6, 87]-NRT-code)	[i]
5	Linear OOA(2¹⁹⁴, 100, F₂, 2, 104) (dual of [(100, 2), 6, 105]-NRT-code)	[i]
6	Linear OOA(2²²⁸, 117, F₂, 2, 122) (dual of [(117, 2), 6, 123]-NRT-code)	[i]