MinT - Information on Result #2992445

Information on Result #2992445

Linear OOA(2²⁵³, 32, F₂, 8, 232) (dual of [(32, 8), 3, 233]-NRT-code), using strength reduction based on linear OOA(2²⁵³, 32, F₂, 8, 235) (dual of [(32, 8), 3, 236]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2²¹, 3, F₂, 8, 21) (dual of [(3, 8), 3, 22]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(8;3,2) [i]
2. linear OOA(2²²⁹, 29, F₂, 8, 213) (dual of [(29, 8), 3, 214]-NRT-code), using
  - 8 step truncation [i] based on linear OOA(2²³⁷, 30, F₂, 8, 221) (dual of [(30, 8), 3, 222]-NRT-code), using
    - repeating each code word 6 times [i] based on linear OOA(2³⁷, 5, F₂, 8, 36) (dual of [(5, 8), 3, 37]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(8;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(2²⁵², 31, F₂, 8, 231)	[i]	Truncation for OOAs
2	Linear OOA(2²⁵¹, 31, F₂, 8, 230)	[i]
3	Linear OOA(2²⁵⁰, 31, F₂, 8, 229)	[i]
4	Linear OOA(2²⁴⁹, 31, F₂, 8, 228)	[i]
5	Linear OOA(2²⁴⁴, 30, F₂, 8, 223)	[i]
6	Linear OOA(2²⁴³, 30, F₂, 8, 222)	[i]
7	Linear OOA(2²⁴², 30, F₂, 8, 221)	[i]
8	Linear OOA(2²⁴¹, 30, F₂, 8, 220)	[i]