Constructions of Constant Dimension Codes

Horlemann-Trautmann, Anna-Lena; Rosenthal, Joachim

doi:10.1007/978-3-319-70293-3_2

Cited by 11 publications

(4 citation statements)

References 40 publications

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“…Here we only mention few general approaches, that give the record codes in the majority of the parameter cases covered in [22], and refer e.g. to the recent survey [28]. Based on Lemma 2.1, in [12] the Echelon-Ferrers construction was introduced, see e.g.…”

Section: Known Constructions and Bounds For Constant-dimension Codesmentioning

confidence: 99%

Combining subspace codes

Cossidente¹,

Kurz²,

Marino³

et al. 2023

AMC

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In the context of constant-dimension subspace codes, an important problem is to determine the largest possible size Aq(n, d; k) of codes whose codewords are k-subspaces of F n q with minimum subspace distance d. Here in order to obtain improved constructions, we investigate several approaches to combine subspace codes. This allow us to present improvements on the lower bounds for constant-dimension subspace codes for many parameters, including

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Section: Known Constructions and Bounds For Constant-dimension Codesmentioning

confidence: 99%

Combining subspace codes

Cossidente¹,

Kurz²,

Marino³

et al. 2023

AMC

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“…In this subsection, we recall the definition of subspace codes and explain a connection between the Schubert cells of the Grassmannian and Ferrers diagram rank-metric codes. For a detailed treatment of the topic, we refer the interested reader to the surveys [13,15].…”

Section: Subspace Codesmentioning

confidence: 99%

Construction of LDPC convolutional codes via difference triangle sets

Alfarano

Lieb

Rosenthal

2021

Des. Codes Cryptogr.

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In this paper, a construction of $$(n,k,\delta )$$ ( n , k , δ ) LDPC convolutional codes over arbitrary finite fields, which generalizes the work of Robinson and Bernstein and the later work of Tong is provided. The sets of integers forming a (k, w)-(weak) difference triangle set are used as supports of some columns of the sliding parity-check matrix of an $$(n,k,\delta )$$ ( n , k , δ ) convolutional code, where $$n\in {\mathbb {N}}$$ n ∈ N , $$n>k$$ n > k . The parameters of the convolutional code are related to the parameters of the underlying difference triangle set. In particular, a relation between the free distance of the code and w is established as well as a relation between the degree of the code and the scope of the difference triangle set. Moreover, we show that some conditions on the weak difference triangle set ensure that the Tanner graph associated to the sliding parity-check matrix of the convolutional code is free from $$2\ell $$ 2 ℓ -cycles not satisfying the full rank condition over any finite field. Finally, we relax these conditions and provide a lower bound on the field size, depending on the parity of $$\ell $$ ℓ , that is sufficient to still avoid $$2\ell $$ 2 ℓ -cycles. This is important for improving the performance of a code and avoiding the presence of low-weight codewords and absorbing sets.

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“…The source sends a (basis of a) vector space, the receiver gathers a (basis of a) vector space possibly affected by noise. Subspace codes gained a lot of attention in the past years; see for instance [19] and references therein. In many of the previous works, constant dimension codes are considered, i.e.…”

Section: Introductionmentioning

confidence: 99%