MinT - Information on Result #2765149

Information on Result #2765149

Linear OOA(2²¹², 63, F₂, 4, 110) (dual of [(63, 4), 40, 111]-NRT-code), using strength reduction based on linear OOA(2²¹², 63, F₂, 4, 111) (dual of [(63, 4), 40, 112]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹³, 21, F₃₂, 13) (dual of [21, 8, 14]-code or 21-arc in PG(12,32)), using
  - discarding factors / shortening the dual code based on linear OA(32¹³, 32, F₃₂, 13) (dual of [32, 19, 14]-code or 32-arc in PG(12,32)), using
    - Reedâ€“Solomon code RS(19,32) [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(2²¹³, 63, F₂, 4, 110) (dual of [(63, 4), 39, 111]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²¹⁴, 63, F₂, 4, 110) (dual of [(63, 4), 38, 111]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²¹¹, 62, F₂, 4, 109) (dual of [(62, 4), 37, 110]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(2²¹⁰, 62, F₂, 4, 108) (dual of [(62, 4), 38, 109]-NRT-code)	[i]
5	Linear OOA(2²⁰⁹, 62, F₂, 4, 107) (dual of [(62, 4), 39, 108]-NRT-code)	[i]
6	Linear OOA(2²⁰⁸, 62, F₂, 4, 106) (dual of [(62, 4), 40, 107]-NRT-code)	[i]
7	Linear OOA(2²⁰⁷, 61, F₂, 4, 105) (dual of [(61, 4), 37, 106]-NRT-code)	[i]
8	Linear OOA(2²⁰⁶, 61, F₂, 4, 104) (dual of [(61, 4), 38, 105]-NRT-code)	[i]
9	Linear OOA(2²⁰⁵, 61, F₂, 4, 103) (dual of [(61, 4), 39, 104]-NRT-code)	[i]
10	Linear OOA(2²⁰⁴, 61, F₂, 4, 102) (dual of [(61, 4), 40, 103]-NRT-code)	[i]