MinT - Information on Result #2295784

Information on Result #2295784

Linear OA(2²²⁷, 276, F₂, 81) (dual of [276, 49, 82]-code), using adding a parity check bit based on linear OA(2²²⁶, 275, F₂, 80) (dual of [275, 49, 81]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(2²⁰⁵, 252, F₂, 81) (dual of [252, 47, 82]-code), using
  - 4 times truncation [i] based on linear OA(2²⁰⁹, 256, F₂, 85) (dual of [256, 47, 86]-code), using
    - an extension C_e(84) of the primitive narrow-sense BCH-code C(I) with length 255Â = 2⁸âˆ’1, defining interval IÂ =Â [1,84], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 85 [i]
2. linear OA(2²⁰⁵, 254, F₂, 66) (dual of [254, 49, 67]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 2²⁰⁵Â > V_b^sâˆ’1(kâˆ’1)Â = 35 274132 412863 054132 229684 711654 639767 724417 705477 243484 858998 [i]
3. linear OA(2¹⁹, 21, F₂, 13) (dual of [21, 2, 14]-code), using
  - repeating each code word 7 times [i] based on linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 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	Linear OA(2²²⁵, 274, F₂, 79) (dual of [274, 49, 80]-code)	[i]		Truncation
2	Linear OA(2²²⁴, 273, F₂, 78) (dual of [273, 49, 79]-code)	[i]		Truncation