MinT - Information on Result #2764545

Information on Result #2764545

Linear OOA(2²⁰³, 57, F₂, 4, 118) (dual of [(57, 4), 25, 119]-NRT-code), using strength reduction based on linear OOA(2²⁰³, 57, F₂, 4, 119) (dual of [(57, 4), 25, 120]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹⁴, 19, F₃₂, 14) (dual of [19, 5, 15]-code or 19-arc in PG(13,32)), using
  - discarding factors / shortening the dual code based on linear OA(32¹⁴, 32, F₃₂, 14) (dual of [32, 18, 15]-code or 32-arc in PG(13,32)), using
    - Reedâ€“Solomon code RS(18,32) [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(2²⁰⁴, 57, F₂, 4, 118) (dual of [(57, 4), 24, 119]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²⁰⁵, 57, F₂, 4, 118) (dual of [(57, 4), 23, 119]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁰², 56, F₂, 4, 117) (dual of [(56, 4), 22, 118]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(2²⁰¹, 56, F₂, 4, 116) (dual of [(56, 4), 23, 117]-NRT-code)	[i]
5	Linear OOA(2²⁰⁰, 56, F₂, 4, 115) (dual of [(56, 4), 24, 116]-NRT-code)	[i]
6	Linear OOA(2¹⁹⁹, 56, F₂, 4, 114) (dual of [(56, 4), 25, 115]-NRT-code)	[i]
7	Linear OOA(2¹⁹⁷, 55, F₂, 4, 112) (dual of [(55, 4), 23, 113]-NRT-code)	[i]
8	Linear OOA(2¹⁹⁶, 55, F₂, 4, 111) (dual of [(55, 4), 24, 112]-NRT-code)	[i]
9	Linear OOA(2¹⁹⁵, 55, F₂, 4, 110) (dual of [(55, 4), 25, 111]-NRT-code)	[i]