MinT - Information on Result #1513782

Information on Result #1513782

Linear OOA(2¹⁷⁷, 2958766, F₂, 3, 12) (dual of [(2958766, 3), 8876121, 13]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁷⁷, 2958766, F₂, 2, 12) (dual of [(2958766, 2), 5917355, 13]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁷⁷, 4198397, F₂, 2, 12) (dual of [(4198397, 2), 8396617, 13]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2¹⁷⁵, 4198396, F₂, 2, 12) (dual of [(4198396, 2), 8396617, 13]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2³⁷, 4095, F₂, 2, 6) (dual of [(4095, 2), 8153, 7]-NRT-code), using
      - OOAs constructed from BCH codes [i]
    2. linear OOA(2¹³⁸, 4194301, F₂, 2, 12) (dual of [(4194301, 2), 8388464, 13]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(2¹³⁸, 8388602, F₂, 12) (dual of [8388602, 8388464, 13]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹³⁸, large, F₂, 12) (dual of [large, large−138, 13]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Mode: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2¹⁷⁷, 1479383, F₂, 6, 12) (dual of [(1479383, 6), 8876121, 13]-NRT-code)	[i]		OOA Folding