MinT - Information on Result #1443050

Information on Result #1443050

Linear OOA(7¹¹⁰, 15883, F₇, 2, 25) (dual of [(15883, 2), 31656, 26]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(7¹¹⁰, 15883, F₇, 25) (dual of [15883, 15773, 26]-code), using

discarding factors / shortening the dual code based on linear OA(7¹¹⁰, 16826, F₇, 25) (dual of [16826, 16716, 26]-code), using
- 1 times code embedding in larger space [i] based on linear OA(7¹⁰⁹, 16825, F₇, 25) (dual of [16825, 16716, 26]-code), using
  - constructionÂ X applied to C_e(24) âŠ‚ C_e(21) [i] based on
    1. linear OA(7¹⁰⁶, 16807, F₇, 25) (dual of [16807, 16701, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 16806Â = 7⁵âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
    2. linear OA(7⁹¹, 16807, F₇, 22) (dual of [16807, 16716, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 16806Â = 7⁵âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
    3. linear OA(7³, 18, F₇, 2) (dual of [18, 15, 3]-code), using
      - discarding factors / shortening the dual code based on linear OA(7³, 48, F₇, 2) (dual of [48, 45, 3]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 48Â = 7²âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [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(7¹¹⁰, 7941, F₇, 3, 25) (dual of [(7941, 3), 23713, 26]-NRT-code)	[i]		OOA Folding