Abstract
A subspace code is a nonempty set of subspaces of a vector space \({\mathbb {F}}^n_q\). Linear codes with complementary duals, or LCD codes, are linear codes whose intersection with their duals is trivial. In this paper, we introduce a notion of LCD subspace codes. We show that the minimum distance decoding problem for an LCD subspace code reduces to a problem that is simpler than for a general subspace code. Further, we show that under some conditions equitable partitions of association schemes yield such LCD subspace codes and as an illustration of the method give some examples from distance-regular graphs. We also give constructions from mutually unbiased weighing matrices, that include constructions from mutually unbiased Hadamard matrices.
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The authors thank the anonymous referees for their helpful comments that improved the presentation of the paper.
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This work has been fully supported by Croatian Science Foundation under the Project 5713.
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Communicated by V. D. Tonchev.
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Crnković, D., Švob, A. LCD subspace codes. Des. Codes Cryptogr. 91, 3215–3226 (2023). https://doi.org/10.1007/s10623-023-01251-3
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DOI: https://doi.org/10.1007/s10623-023-01251-3