MinT - Information on Result #1120920

Information on Result #1120920

Linear OOA(2²⁵¹, 51, F₂, 5, 210) (dual of [(51, 5), 4, 211]-NRT-code), using juxtaposition based on

linear OOA(2¹⁶, 4, F₂, 5, 15) (dual of [(4, 5), 4, 16]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹⁶, 5, F₂, 5, 15) (dual of [(5, 5), 9, 16]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(5;F,9P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
    - an explicitly constructive algebraic function field [i]
linear OOA(2²³¹, 47, F₂, 5, 194) (dual of [(47, 5), 4, 195]-NRT-code), using
- strength reduction [i] based on linear OOA(2²³¹, 47, F₂, 5, 196) (dual of [(47, 5), 4, 197]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(2²¹, 5, F₂, 5, 20) (dual of [(5, 5), 4, 21]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(5;F,4P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5 (see above)
    2. linear OOA(2²⁰⁶, 42, F₂, 5, 175) (dual of [(42, 5), 4, 176]-NRT-code), using
      - juxtaposition [i] based on
        linear OOA(2²¹, 5, F₂, 5, 20) (dual of [(5, 5), 4, 21]-NRT-code) (see above)
        linear OOA(2¹⁸¹, 37, F₂, 5, 154) (dual of [(37, 5), 4, 155]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2²¹, 5, F₂, 5, 20) (dual of [(5, 5), 4, 21]-NRT-code) (see above)
        linear OOA(2¹⁵⁶, 32, F₂, 5, 133) (dual of [(32, 5), 4, 134]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2²¹, 5, F₂, 5, 20) (dual of [(5, 5), 4, 21]-NRT-code) (see above)
        linear OOA(2¹³¹, 27, F₂, 5, 112) (dual of [(27, 5), 4, 113]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2²¹, 5, F₂, 5, 20) (dual of [(5, 5), 4, 21]-NRT-code) (see above)
        linear OOA(2¹⁰⁶, 22, F₂, 5, 91) (dual of [(22, 5), 4, 92]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2²¹, 5, F₂, 5, 20) (dual of [(5, 5), 4, 21]-NRT-code) (see above)
        linear OOA(2⁸¹, 17, F₂, 5, 70) (dual of [(17, 5), 4, 71]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2²¹, 5, F₂, 5, 20) (dual of [(5, 5), 4, 21]-NRT-code) (see above)
        linear OOA(2⁵⁶, 12, F₂, 5, 49) (dual of [(12, 5), 4, 50]-NRT-code), using
        repeating each code word 2 times [i] based on linear OOA(2²⁶, 6, F₂, 5, 24) (dual of [(6, 5), 4, 25]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(5;F,5P) [i] based on function field F/F₂ with g(F) = 2 and N(F) ≥ 6, 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(2²⁵¹, 51, F₂, 5, 209) (dual of [(51, 5), 4, 210]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2²⁵¹, 51, F₂, 5, 208) (dual of [(51, 5), 4, 209]-NRT-code)	[i]
3	Linear OOA(2²⁵¹, 51, F₂, 5, 207) (dual of [(51, 5), 4, 208]-NRT-code)	[i]
4	Linear OOA(2²⁵¹, 51, F₂, 5, 206) (dual of [(51, 5), 4, 207]-NRT-code)	[i]
5	Linear OOA(2²⁵¹, 51, F₂, 5, 205) (dual of [(51, 5), 4, 206]-NRT-code)	[i]
6	Linear OOA(2²⁵¹, 51, F₂, 5, 204) (dual of [(51, 5), 4, 205]-NRT-code)	[i]