MinT - Information on Result #2848698

Information on Result #2848698

Linear OOA(2²⁵⁷, 52, F₂, 5, 222) (dual of [(52, 5), 3, 223]-NRT-code), using strength reduction based on linear OOA(2²⁵⁷, 52, F₂, 5, 223) (dual of [(52, 5), 3, 224]-NRT-code), using

repeating each code word 4 times [i] based on linear OOA(2⁶², 13, F₂, 5, 55) (dual of [(13, 5), 3, 56]-NRT-code), using
- strength reduction [i] based on linear OOA(2⁶², 13, F₂, 5, 56) (dual of [(13, 5), 3, 57]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(2¹², 3, F₂, 5, 12) (dual of [(3, 5), 3, 13]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(5;3,2) [i]
    2. linear OOA(2⁴⁷, 10, F₂, 5, 43) (dual of [(10, 5), 3, 44]-NRT-code), using
      - repeating each code word 2 times [i] based on linear OOA(2²², 5, F₂, 5, 21) (dual of [(5, 5), 3, 22]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(5;F,3P) [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(2²⁵⁶, 51, F₂, 5, 221)	[i]	Truncation for OOAs
2	Linear OOA(2²⁵¹, 50, F₂, 5, 216)	[i]
3	Linear OOA(2²⁴⁶, 49, F₂, 5, 211)	[i]
4	Linear OOA(2²⁴³, 49, F₂, 5, 208) (dual of [(49, 5), 2, 209]-NRT-code)	[i]
5	Linear OOA(2²⁴², 49, F₂, 5, 207) (dual of [(49, 5), 3, 208]-NRT-code)	[i]
6	Linear OOA(2²⁴¹, 48, F₂, 5, 206)	[i]
7	Linear OOA(2²³⁶, 47, F₂, 5, 201)	[i]
8	Linear OOA(2²³³, 47, F₂, 5, 198) (dual of [(47, 5), 2, 199]-NRT-code)	[i]