MinT - Information on Result #1517884

Information on Result #1517884

Linear OOA(2²³⁴, 980, F₂, 3, 41) (dual of [(980, 3), 2706, 42]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²³⁴, 980, F₂, 2, 41) (dual of [(980, 2), 1726, 42]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²³⁴, 1047, F₂, 2, 41) (dual of [(1047, 2), 1860, 42]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2²³⁴, 2094, F₂, 41) (dual of [2094, 1860, 42]-code), using
  - constructionÂ X applied to C_e(40) âŠ‚ C_e(34) [i] based on
    1. linear OA(2²²¹, 2048, F₂, 41) (dual of [2048, 1827, 42]-code), using an extension C_e(40) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,40], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 41 [i]
    2. linear OA(2¹⁸⁸, 2048, F₂, 35) (dual of [2048, 1860, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
    3. linear OA(2¹³, 46, F₂, 5) (dual of [46, 33, 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(2²³⁴, 490, F₂, 5, 41) (dual of [(490, 5), 2216, 42]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²³⁴, 490, F₂, 6, 41) (dual of [(490, 6), 2706, 42]-NRT-code)	[i]		OOA Folding