MinT - Information on Result #2767600

Information on Result #2767600

Linear OOA(2²⁵⁰, 65, F₂, 4, 178) (dual of [(65, 4), 10, 179]-NRT-code), using strength reduction based on linear OOA(2²⁵⁰, 65, F₂, 4, 179) (dual of [(65, 4), 10, 180]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹¹, 13, F₃₂, 11) (dual of [13, 2, 12]-code or 13-arc in PG(10,32)), using
  - discarding factors / shortening the dual code based on linear OA(32¹¹, 32, F₃₂, 11) (dual of [32, 21, 12]-code or 32-arc in PG(10,32)), using
    - Reedâ€“Solomon code RS(21,32) [i]
2. linear OOA(2¹⁵, 5, F₂, 4, 14) (dual of [(5, 4), 5, 15]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;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(2²⁵⁴, 66, F₂, 4, 178) (dual of [(66, 4), 10, 179]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²⁵⁸, 67, F₂, 4, 178) (dual of [(67, 4), 10, 179]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(2²⁵¹, 65, F₂, 4, 178) (dual of [(65, 4), 9, 179]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(2²⁴⁷, 64, F₂, 4, 175) (dual of [(64, 4), 9, 176]-NRT-code)	[i]	Truncation for OOAs
5	Linear OOA(2²⁴⁶, 64, F₂, 4, 174) (dual of [(64, 4), 10, 175]-NRT-code)	[i]
6	Linear OOA(2²⁴⁴, 63, F₂, 4, 172) (dual of [(63, 4), 8, 173]-NRT-code)	[i]
7	Linear OOA(2²⁴³, 63, F₂, 4, 171) (dual of [(63, 4), 9, 172]-NRT-code)	[i]
8	Linear OOA(2²⁴², 63, F₂, 4, 170) (dual of [(63, 4), 10, 171]-NRT-code)	[i]
9	Linear OOA(2²⁴⁰, 62, F₂, 4, 168) (dual of [(62, 4), 8, 169]-NRT-code)	[i]
10	Linear OOA(2²³⁹, 62, F₂, 4, 167) (dual of [(62, 4), 9, 168]-NRT-code)	[i]
11	Linear OOA(2²³⁸, 62, F₂, 4, 166) (dual of [(62, 4), 10, 167]-NRT-code)	[i]
12	Linear OOA(2²³⁵, 61, F₂, 4, 163) (dual of [(61, 4), 9, 164]-NRT-code)	[i]
13	Linear OOA(2²³⁴, 61, F₂, 4, 162) (dual of [(61, 4), 10, 163]-NRT-code)	[i]