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Two new constructions of cyclic subspace codes via Sidon spaces
A subspace of a finite field is called a Sidon space if the product of any two of its nonzero elements is unique up to a scalar multiplier from the...
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A new construction of cyclic subspace codes
Subspace codes have attracted a lot of attention in the last few decades due to their applications in noncoherent linear network coding, in...
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Cyclic constant dimension subspace codes via the sum of Sidon spaces
Subspace codes are of great use in noncoherent linear network coding (Katti et al in ACM SIGCOMM Comput Commun Rev 38(4):401–412, 2008; Kötter and...
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Distance Distributions of Cyclic Orbit Codes
The distance distribution of a code is the vector whose i th entry is the number of pairs of codewords with distance i . We investigate the structure...
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New constructions of constant dimension subspace codes with large sizes
Subspace codes have important applications in random network coding. It is a classical problem to construct subspace codes where both their size and...
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Submodule codes as spherical codes in buildings
We give a generalization of subspace codes by means of codes of modules over finite commutative chain rings. We define a new class of Sperner codes...
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Further constructions of cyclic subspace codes
Subspace codes, especially cyclic subspace codes, have attracted a wide attention in the past few decades due to their applications in error...
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Abelian and consta-Abelian polyadic codes over affine algebras with a finite commutative chain coefficient ring
This paper studies Abelian and consta-Abelian polyadic codes over rings defined as affine algebras over chain rings. For this purpose, we use the...
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Moderate Classical McEliece Keys from Quasi-Centrosymmetric Goppa Codes
As the development of quantum machines is booming and would threaten our standard cryptography algorithms, a transition period is necessary for the...
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MacWilliams extension property for arbitrary weights on linear codes over module alphabets
The first author recently proved the extension theorem for linear codes over integer residue rings equipped with the Lee or the Euclidean weight by...
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The Projective General Linear Group PGL(2, \(5^m\) ) and Linear Codes of Length \(5^m+1\)
The importance of interactions between groups, linear codes and t-designs has been well recognized for decades. Linear codes that are invariant under...
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Equidistant permutation group codes
We study permutation codes which are groups and all of whose non-identity code elements have the same number of fixed points. It follows that over...
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Quadratic residue codes, rank three groups and PBIBDs
The automorphism group of the Zetterberg code Z of length 17 (also a quadratic residue code) is a rank three group whose orbits on the coordinate...
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On Codes and Learning with Errors over Function Fields
It is a long standing open problem to find search to decision reductions for structured versions of the decoding problem of linear codes. Such...
