MinT - Information on Result #2767799

Information on Result #2767799

Linear OOA(2²⁵², 84, F₂, 4, 103) (dual of [(84, 4), 84, 104]-NRT-code), using strength reduction based on linear OOA(2²⁵², 84, F₂, 4, 104) (dual of [(84, 4), 84, 105]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(64¹⁴, 28, F₆₄, 14) (dual of [28, 14, 15]-code or 28-arc in PG(13,64)), using
  - discarding factors / shortening the dual code based on linear OA(64¹⁴, 64, F₆₄, 14) (dual of [64, 50, 15]-code or 64-arc in PG(13,64)), using
    - Reedâ€“Solomon code RS(50,64) [i]
2. linear OOA(2⁶, 3, F₂, 4, 6) (dual of [(3, 4), 6, 7]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(4;6,2) [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(2²⁵⁶, 85, F₂, 4, 103) (dual of [(85, 4), 84, 104]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²⁵³, 84, F₂, 4, 103) (dual of [(84, 4), 83, 104]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁵⁴, 84, F₂, 4, 103) (dual of [(84, 4), 82, 104]-NRT-code)	[i]
4	Linear OOA(2²⁵⁵, 84, F₂, 4, 103) (dual of [(84, 4), 81, 104]-NRT-code)	[i]
5	Linear OOA(2²⁵¹, 83, F₂, 4, 102) (dual of [(83, 4), 81, 103]-NRT-code)	[i]	Truncation for OOAs
6	Linear OOA(2²⁵⁰, 83, F₂, 4, 101) (dual of [(83, 4), 82, 102]-NRT-code)	[i]
7	Linear OOA(2²⁴⁹, 83, F₂, 4, 100) (dual of [(83, 4), 83, 101]-NRT-code)	[i]
8	Linear OOA(2²⁴⁸, 83, F₂, 4, 99) (dual of [(83, 4), 84, 100]-NRT-code)	[i]
9	Linear OOA(2²⁴⁷, 82, F₂, 4, 98) (dual of [(82, 4), 81, 99]-NRT-code)	[i]
10	Linear OOA(2²⁵², 42, F₂, 7, 103) (dual of [(42, 7), 42, 104]-NRT-code)	[i]	OOA Folding
11	Linear OOA(2²⁵², 42, F₂, 8, 103) (dual of [(42, 8), 84, 104]-NRT-code)	[i]	OOA Folding