MinT - Information on Result #2618703

Information on Result #2618703

Linear OOA(2²⁴⁰, 90, F₂, 3, 128) (dual of [(90, 3), 30, 129]-NRT-code), using strength reduction based on linear OOA(2²⁴⁰, 90, F₂, 3, 129) (dual of [(90, 3), 30, 130]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹², 18, F₃₂, 12) (dual of [18, 6, 13]-code or 18-arc in PG(11,32)), using
  - discarding factors / shortening the dual code based on linear OA(32¹², 32, F₃₂, 12) (dual of [32, 20, 13]-code or 32-arc in PG(11,32)), using
    - Reedâ€“Solomon code RS(20,32) [i]
2. linear OOA(2¹⁰, 5, F₂, 3, 9) (dual of [(5, 3), 5, 10]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,5P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
    - an explicitly constructive algebraic function field [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(2²⁴³, 91, F₂, 3, 128) (dual of [(91, 3), 30, 129]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²⁴¹, 90, F₂, 3, 128) (dual of [(90, 3), 29, 129]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²³⁹, 89, F₂, 3, 127) (dual of [(89, 3), 28, 128]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(2²³⁸, 89, F₂, 3, 126) (dual of [(89, 3), 29, 127]-NRT-code)	[i]
5	Linear OOA(2²³⁷, 89, F₂, 3, 125) (dual of [(89, 3), 30, 126]-NRT-code)	[i]
6	Linear OOA(2²³⁶, 88, F₂, 3, 124) (dual of [(88, 3), 28, 125]-NRT-code)	[i]
7	Linear OOA(2²³⁵, 88, F₂, 3, 123) (dual of [(88, 3), 29, 124]-NRT-code)	[i]
8	Linear OOA(2²³⁴, 88, F₂, 3, 122) (dual of [(88, 3), 30, 123]-NRT-code)	[i]
9	Linear OOA(2²³², 87, F₂, 3, 120) (dual of [(87, 3), 29, 121]-NRT-code)	[i]
10	Linear OOA(2²³¹, 87, F₂, 3, 119) (dual of [(87, 3), 30, 120]-NRT-code)	[i]
11	Linear OOA(2²⁴⁰, 45, F₂, 6, 128) (dual of [(45, 6), 30, 129]-NRT-code)	[i]	OOA Folding