MinT - Information on Result #2768169

Information on Result #2768169

Linear OOA(2²⁵⁸, 84, F₂, 4, 110) (dual of [(84, 4), 78, 111]-NRT-code), using strength reduction based on linear OOA(2²⁵⁸, 84, F₂, 4, 111) (dual of [(84, 4), 78, 112]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(64¹⁵, 28, F₆₄, 15) (dual of [28, 13, 16]-code or 28-arc in PG(14,64)), using
  - discarding factors / shortening the dual code based on linear OA(64¹⁵, 64, F₆₄, 15) (dual of [64, 49, 16]-code or 64-arc in PG(14,64)), using
    - Reedâ€“Solomon code RS(49,64) [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(2²⁵⁹, 84, F₂, 4, 110) (dual of [(84, 4), 77, 111]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²⁶⁰, 84, F₂, 4, 110) (dual of [(84, 4), 76, 111]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁵⁷, 83, F₂, 4, 109) (dual of [(83, 4), 75, 110]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(2²⁵⁶, 83, F₂, 4, 108) (dual of [(83, 4), 76, 109]-NRT-code)	[i]
5	Linear OOA(2²⁵⁵, 83, F₂, 4, 107) (dual of [(83, 4), 77, 108]-NRT-code)	[i]
6	Linear OOA(2²⁵⁴, 83, F₂, 4, 106) (dual of [(83, 4), 78, 107]-NRT-code)	[i]
7	Linear OOA(2²⁵³, 82, F₂, 4, 105) (dual of [(82, 4), 75, 106]-NRT-code)	[i]
8	Linear OOA(2²⁵⁸, 42, F₂, 7, 110) (dual of [(42, 7), 36, 111]-NRT-code)	[i]	OOA Folding
9	Linear OOA(2²⁵⁸, 42, F₂, 8, 110) (dual of [(42, 8), 78, 111]-NRT-code)	[i]	OOA Folding