MinT - Information on Result #1705312

Information on Result #1705312

Linear OOA(2²³⁹, 3757, F₂, 8, 33) (dual of [(3757, 8), 29817, 34]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²³⁹, 3757, F₂, 4, 33) (dual of [(3757, 4), 14789, 34]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²³⁹, 4110, F₂, 4, 33) (dual of [(4110, 4), 16201, 34]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2²³⁹, 16440, F₂, 33) (dual of [16440, 16201, 34]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(2²³⁸, 16439, F₂, 33) (dual of [16439, 16201, 34]-code), using
    - constructionÂ X applied to C_e(32) âŠ‚ C_e(26) [i] based on
      1. linear OA(2²²⁵, 16384, F₂, 33) (dual of [16384, 16159, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
      2. linear OA(2¹⁸³, 16384, F₂, 27) (dual of [16384, 16201, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
      3. linear OA(2¹³, 55, F₂, 5) (dual of [55, 42, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹³, 63, F₂, 5) (dual of [63, 50, 6]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]

Mode: 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		This result only	Method
1	Linear OOA(2²³⁹, 1878, F₂, 40, 33) (dual of [(1878, 40), 74881, 34]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row