MinT - Information on Result #1615261

Information on Result #1615261

Linear OOA(256¹⁶, 32770, F₂₅₆, 4, 8) (dual of [(32770, 4), 131064, 9]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256¹⁶, 32770, F₂₅₆, 2, 8) (dual of [(32770, 2), 65524, 9]-NRT-code), using

OOA 2-folding [i] based on linear OA(256¹⁶, 65540, F₂₅₆, 8) (dual of [65540, 65524, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(256¹⁶, 65541, F₂₅₆, 8) (dual of [65541, 65525, 9]-code), using
  - constructionÂ X applied to C_e(7) âŠ‚ C_e(5) [i] based on
    1. linear OA(256¹⁵, 65536, F₂₅₆, 8) (dual of [65536, 65521, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
    2. linear OA(256¹¹, 65536, F₂₅₆, 6) (dual of [65536, 65525, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
    3. linear OA(256¹, 5, F₂₅₆, 1) (dual of [5, 4, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(256¹, s, F₂₅₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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	OOA(128¹⁹, 32770, S₁₂₈, 4, 8)	[i]		Discarding Parts of the Base for OOAs
2	Linear OOA(256¹⁶, 32769, F₂₅₆, 5, 8) (dual of [(32769, 5), 163829, 9]-NRT-code)	[i]		OOA Stacking with Additional Row
3	Linear OOA(256¹⁶, 32769, F₂₅₆, 6, 8) (dual of [(32769, 6), 196598, 9]-NRT-code)	[i]
4	Linear OOA(256¹⁶, 32769, F₂₅₆, 12, 8) (dual of [(32769, 12), 393212, 9]-NRT-code)	[i]