Further constructions of large cyclic subspace codes via Sidon spaces

Zhang, He; Tang, Chunming

doi:10.1016/j.laa.2022.12.011

Cited by 6 publications

(2 citation statements)

References 26 publications

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“…In the first family, we find the examples in [40,Constructions 11 and 15], [50,Lemma 3.1], [24, Lemmas 4.1 and 4.2] and [51,Lemma 2.4], in the second one we find examples in [53, Theorems 3.2 and 3.6], [50, Lemma 3.3, Theorems 3.5 and 3.13], [24,Theorems 4.5,4.7,4.9,, [49, Lemma 5 and Theorem 6], [52, Theorems 3.1 and 3.2] and [16,Theorem 3.3], and for the last family we can find examples in [9, Corollary 4 and Section IIIA] and [41,Section 7.3].…”

Section: Introductionmentioning

confidence: 99%

Constructions and equivalence of Sidon spaces

Castello,

Polverino,

Santonastaso

et al. 2023

J Algebr Comb

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Sidon spaces have been introduced by Bachoc et al. (in: Mathematical Proceedings of the Cambridge Philosophical Society, Cambridge University Press, 2017) as the q-analogue of Sidon sets. The interest on Sidon spaces has increased quickly, especially after the work of Roth et al. (IEEE Trans Inform Theory 64(6):4412–4422, 2017), in which they highlighted the correspondence between Sidon spaces and cyclic subspace codes. Up to now, the known constructions of Sidon Spaces may be divided in three families: the ones contained in the sum of two multiplicative cosets of a fixed subfield of $$\mathbb {F}_{q^n}$$ F q n , the ones contained in the sum of more than two multiplicative cosets of a fixed subfield of $$\mathbb {F}_{q^n}$$ F q n and finally the ones obtained as the kernel of subspace polynomials. In this paper, we will mainly focus on the first class of examples, for which we provide characterization results and we will show some new examples, arising also from some well-known combinatorial objects. Moreover, we will give a quite natural definition of equivalence among Sidon spaces, which relies on the notion of equivalence of cyclic subspace codes and we will discuss about the equivalence of the known examples.

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Section: Introductionmentioning

confidence: 99%

Constructions and equivalence of Sidon spaces

Castello,

Polverino,

Santonastaso

et al. 2023

J Algebr Comb

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show abstract

“…Their cyclic subspace codes have larger sizes than those in literatures. For more constructions of Sidon spaces and cyclic subspace codes, we refer to [14][15][16][17][18][19].…”

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confidence: 99%

A new construction of cyclic subspace codes

Han,

Cao

2024

Preprint

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Subspace codes have attracted a lot of attention in the last few decades due to their applications innoncoherent linear network coding, in particular cyclic subspace codes can be encoded and decoded moreefficiently because of their special algebraic structure. Using the union of several cyclic subspace codes, wepresent a family of cyclic subspace codes with minimum distance 2k − 2 and size seqk(qk − 1)s−1(qn − 1), where k|n, n/k ≥ 2s + 1, s ≥ 2, e = ⌈n/2sk⌉ − 1.

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Two new constructions of cyclic subspace codes via Sidon spaces

Yu,

2024

Des. Codes Cryptogr.

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Further constructions of large cyclic subspace codes via Sidon spaces

Cited by 6 publications

References 26 publications

Constructions and equivalence of Sidon spaces

Constructions and equivalence of Sidon spaces

A new construction of cyclic subspace codes

Two new constructions of cyclic subspace codes via Sidon spaces

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