MinT - Information on Result #991121

Information on Result #991121

Linear OOA(81⁷⁰, 4194301, F₈₁, 3, 13) (dual of [(4194301, 3), 12582833, 14]-NRT-code), using OOA 2-folding based on linear OOA(81⁷⁰, 8388602, F₈₁, 2, 13) (dual of [(8388602, 2), 16777134, 14]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(81²¹, 4194301, F₈₁, 2, 6) (dual of [(4194301, 2), 8388581, 7]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(81²¹, 8388602, F₈₁, 6) (dual of [8388602, 8388581, 7]-code), using
    - discarding factors / shortening the dual code based on linear OA(81²¹, large, F₈₁, 6) (dual of [large, large−21, 7]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
2. linear OOA(81⁴⁹, 4194301, F₈₁, 2, 13) (dual of [(4194301, 2), 8388553, 14]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(81⁴⁹, 8388602, F₈₁, 13) (dual of [8388602, 8388553, 14]-code), using
    - discarding factors / shortening the dual code based on linear OA(81⁴⁹, large, F₈₁, 13) (dual of [large, large−49, 14]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m 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(9¹⁴⁰, 8388602, F₉, 3, 13) (dual of [(8388602, 3), 25165666, 14]-NRT-code)	[i]		Trace Code for OOAs