MinT - Information on Result #2765467

Information on Result #2765467

Linear OOA(2²¹⁷, 63, F₂, 4, 117) (dual of [(63, 4), 35, 118]-NRT-code), using strength reduction based on linear OOA(2²¹⁷, 63, F₂, 4, 119) (dual of [(63, 4), 35, 120]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹⁴, 21, F₃₂, 14) (dual of [21, 7, 15]-code or 21-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(2²¹⁸, 63, F₂, 4, 117) (dual of [(63, 4), 34, 118]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²¹⁶, 62, F₂, 4, 116) (dual of [(62, 4), 32, 117]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(2²¹⁵, 62, F₂, 4, 115) (dual of [(62, 4), 33, 116]-NRT-code)	[i]
4	Linear OOA(2²¹⁴, 62, F₂, 4, 114) (dual of [(62, 4), 34, 115]-NRT-code)	[i]
5	Linear OOA(2²¹³, 62, F₂, 4, 113) (dual of [(62, 4), 35, 114]-NRT-code)	[i]
6	Linear OOA(2²¹², 61, F₂, 4, 112) (dual of [(61, 4), 32, 113]-NRT-code)	[i]
7	Linear OOA(2²¹¹, 61, F₂, 4, 111) (dual of [(61, 4), 33, 112]-NRT-code)	[i]
8	Linear OOA(2²¹⁰, 61, F₂, 4, 110) (dual of [(61, 4), 34, 111]-NRT-code)	[i]
9	Linear OOA(2²⁰⁹, 61, F₂, 4, 109) (dual of [(61, 4), 35, 110]-NRT-code)	[i]
10	Linear OOA(2²⁰⁸, 60, F₂, 4, 108) (dual of [(60, 4), 32, 109]-NRT-code)	[i]
11	Linear OOA(2²⁰⁷, 60, F₂, 4, 107) (dual of [(60, 4), 33, 108]-NRT-code)	[i]
12	Linear OOA(2²⁰⁶, 60, F₂, 4, 106) (dual of [(60, 4), 34, 107]-NRT-code)	[i]