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CONSTRUCTION OF SELF-DUAL RADICAL 2-CODES OF GIVEN DISTANCE

CAROLIN HANNUSCH

Institute of Mathematics, Debrecen University, 4010 Debrecen, pf.12, Hungary

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and

PIROSKA LAKATOS

Institute of Mathematics, Debrecen University, 4010 Debrecen, pf.12, Hungary

Research supported by Hungarian NFSR (OTKA) grant No. NK-81402.

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https://doi.org/10.1142/S1793830912500528Cited by:0 (Source: Crossref)

Abstract

We prove that for arbitrary n ∈ ℕ and and for a field K of characteristic 2 there exists an abelian group G of order 2ⁿ such that one of the powers of the radical of the group algebra K[G] is a (2ⁿ, 2^n-1, 2^d)-self-dual code. These codes are constructed for abelian groups G with decomposition

where a₁ ≥ 3 and s_i ≥ 0(1 ≤ i ≤ 3).

Keywords:

AMSC: 94B05, 94B60

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