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New constant dimension subspace codes From the Mixed dimension Construction

IEEE TRANSACTIONS ON INFORMATION THEORY 2023年第7期69卷 4333-4344页

作者： Lao, Huimin Chen, Hao Li, Fagang Lyu, Shanxiang Jinan Univ Coll Informat Sci & Technol Cyber Secur Guangzhou 510632 Peoples R China Changzhou Univ Coll Comp Sci & Artifcial Intelligence Changzhou 213164 Peoples R China Changzhou Univ Aliyun Coll Big Data Changzhou 213164 Peoples R China

One of the main problems of subspace coding is to determine the maximal size of a constant dimension subspace code with given parameters. In this paper, we show that mixed dimension subspace codes can be used to construct large constant dimension subspace codes. We introduce a new class of subspace codes called mixed dimension/distance subspace codes. Using such codes, we present two constructions for large constant dimension subspace codes. The problem about the sizes of our constant dimension subspace codes is transformed into finding mixed dimension/distance subspace codes with large dimension distributions. The new constructed codes are the largest known for many sets of parameters. Our method gives at least 136 new lower bounds on the sizes of constant dimension subspace codes.

关键词： constant dimension subspace code mixed dimension/distance subspace code rank-metric code

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subspace code constructions

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RICERCHE DI MATEMATICA 2022年第1期71卷 1-16页

作者： Cossidente, Antonio Marino, Giuseppe Pavese, Francesco Univ Basilicata Dipartimento Matemat Informat & Econ I-85100 Potenza Italy Univ Napoli Federico II Dipartimento Matemat & Applicaz Renato Caccioppol Complesso Univ Monte St Angelo Cupa Nuova Cintia 21 I-80126 Naples Italy Politecn Bari Dipartimento Meccan Matemat & Management Via Orabona 4 I-70125 Bari Italy

We improve on the lower bound of the maximum number of planes of PG(8, q) mutually intersecting in at most one point leading to the following lower bound: A(q) (9, 4;3) >= q(12) + 2q(8) + 2q(7) + q(6) + q(5) + q(4) + 1. We also construct two new nonequivalent (6, (q(3) - 1)(q(2) + q + 1), 4;3) q-constant dimension subspace orbit-codes.

关键词： Circumscribed bundle constant dimension subspace code Singer cyclic group

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New Constructions of subspace codes Using Subsets of MRD codes in Several Blocks

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IEEE TRANSACTIONS ON INFORMATION THEORY 2020年第9期66卷 5317-5321页

作者： Chen, Hao He, Xianmang Weng, Jian Xu, Liqing Jinan Univ Coll Informat Sci & Technol Guangzhou 510632 Peoples R China Jinan Univ Coll Cyber Secur Guangzhou 510632 Peoples R China Dongguan Univ Technol Sch Network Secur Dongguan 523808 Peoples R China

A basic problem for the constant dimension subspace coding is to determine the maximal possible size A(q)(n, d, k) of a set of k-dimensional subspaces in F-q(n) such that the subspace distance satisfies d(U, V) = 2k - 2dim (U boolean AND V) >= d for any two different subspaces U and V in this set. We present two new constructions of constant dimension subspace codes using subsets of maximum rank-distance (MRD) codes in several blocks. This method is firstly applied to the linkage construction and secondly to arbitrary number of blocks of lifting MRD codes. In these two constructions, subsets of MRD codes with bounded ranks play an essential role. The Delsarte theorem about the rank distribution of MRD codes is an important ingredient to count codewords in our constructed constant dimension subspace codes. We give many new lower bounds for A(q)(n, d, k). More than 110 new constant dimension subspace codes better than previously best known codes are constructed

关键词： constant dimension subspace code MRD code q-polynmial

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New constant-dimension subspace codes from Maximum Rank Distance codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2018年第9期64卷 6315-6319页

作者： Xu, Liqing Chen, Hao Hangzhou Dianzi Univ Sch Sci Hangzhou 310018 Zhejiang Peoples R China

The main problem of constant-dimension subspace coding is to determine the maximal possible size A(q) (n, d, k) of a set of k-dimensional subspaces in F-q(n) such that the subspace distance satisfies d(U, V) >= d for any two different subspaces U and V in this set. In this paper, we give a direct construction of constant-dimension subspace codes from two parallel versions of maximum rank-distance codes. The problem about the sizes of our constructed constant-dimension subspace codes is transformed into finding a suitable sufficient condition to restrict number of the roots of L-1(L-2(x)) -x where L-1 and L-2 are q-polynomials over the extension field F-q(n). New lower bounds for A(q) (4k, 2k, 2k), A(q) (4k + 2, 2k, 2k + 1), and A(q) (4k + 2, 2(k -1), 2k + 1) are presented. Many new constant-dimension subspace codes better than previously best known codes with small parameters are constructed.

关键词： constant dimension subspace code MRD code q-polynomial

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Veronese subspace codes

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DESIGNS codeS AND CRYPTOGRAPHY 2016年第3期81卷 445-457页

作者： Cossidente, Antonio Pavese, Francesco Univ Basilicata Dipartimento Matemat Informat & Econ I-85100 Potenza Italy

Using the geometry of quadrics of a projective plane PG(2, q) a family of (6, q(3)(q(2) - 1)(q - 1)/3 + (q(2) + 1) (q(2) + q + 1), 4;3)(q) constant dimension subspace codes is constructed.

关键词： Projective bundle constant dimension subspace code Singer cyclic group Veronese map

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