MinT - Information on Result #2615330

Information on Result #2615330

Linear OOA(2¹⁸⁸, 72, F₂, 3, 100) (dual of [(72, 3), 28, 101]-NRT-code), using strength reduction based on linear OOA(2¹⁸⁸, 72, F₂, 3, 101) (dual of [(72, 3), 28, 102]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16¹⁷, 24, F₁₆, 16) (dual of [24, 7, 17]-code), using
  - extended algebraic-geometric code AG_e(F,7P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
    - a function field by SÃ©mirat [i]
2. linear OOA(2⁵, 3, F₂, 3, 5) (dual of [(3, 3), 4, 6]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(3;4,2) [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(2¹⁹¹, 73, F₂, 3, 100) (dual of [(73, 3), 28, 101]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2¹⁸⁹, 72, F₂, 3, 100) (dual of [(72, 3), 27, 101]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2¹⁹⁰, 72, F₂, 3, 100) (dual of [(72, 3), 26, 101]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(2¹⁸⁷, 71, F₂, 3, 99) (dual of [(71, 3), 26, 100]-NRT-code)	[i]	Truncation for OOAs
5	Linear OOA(2¹⁸⁶, 71, F₂, 3, 98) (dual of [(71, 3), 27, 99]-NRT-code)	[i]
6	Linear OOA(2¹⁸⁵, 71, F₂, 3, 97) (dual of [(71, 3), 28, 98]-NRT-code)	[i]
7	Linear OOA(2¹⁸⁴, 70, F₂, 3, 96) (dual of [(70, 3), 26, 97]-NRT-code)	[i]
8	Linear OOA(2¹⁸³, 70, F₂, 3, 95) (dual of [(70, 3), 27, 96]-NRT-code)	[i]
9	Linear OOA(2¹⁸², 70, F₂, 3, 94) (dual of [(70, 3), 28, 95]-NRT-code)	[i]
10	Linear OOA(2¹⁸¹, 69, F₂, 3, 93) (dual of [(69, 3), 26, 94]-NRT-code)	[i]
11	Linear OOA(2¹⁸⁰, 69, F₂, 3, 92) (dual of [(69, 3), 27, 93]-NRT-code)	[i]
12	Linear OOA(2¹⁷⁸, 68, F₂, 3, 90) (dual of [(68, 3), 26, 91]-NRT-code)	[i]
13	Linear OOA(2¹⁸⁸, 36, F₂, 6, 100) (dual of [(36, 6), 28, 101]-NRT-code)	[i]	OOA Folding