Network coding and subspace designs. (2018)

• Record Type: Book
• Further Information: Note: Marcus Greferath, Mario Osvin Pavčević, Natalia Silberstein, María Ángeles Vázquez-Castro, editors.
• Editors: Greferath, Marcus; Pavčević, Mario Osvin; Silberstein, Natalia; Vázquez-Castro, María Ángeles
• Contents: Intro; Foreword; Preface; Contents; Subspace Codes and Rank Metric Codes; Codes Endowed with the Rank Metric; 1 Rank-Metric Codes; 2 MacWilliams Identities for the Rank Metric; 3 MRD Codes; 4 Rank-Metric Anticodes; References; Constructions of Constant Dimension Codes; 1 Introduction; 2 Remarks on the Geometry of the Finite Grassmann Variety; 3 Spread Codes, Partial Spread Codes and Equidistant Codes; 4 Constructions Based on (Ferrers Diagram) Rank-Metric Codes; 5 Orbit Codes; 5.1 Single Orbits; 5.2 Unions of Orbits; 6 New from Old Codes; 7 Final Remarks; References. Constructions of Cyclic Subspace Codes and Maximum Rank Distance Codes1 Introduction; 1.1 Linearized Polynomials; 1.2 Subspace Codes; 1.3 Rank Metric Codes; 2 Construction of Cyclic Subspace Codes; 2.1 A Construction Including Many Full Length Orbits; 2.2 Generalization to Other Small Minimum Distances; 2.3 Possible Values for the Length Parameter; 3 Construction of Maximum Rank Distance Codes; 3.1 Linear MRD Codes; 3.2 Additive MRD Codes; 3.3 A Family of Non-additive MRD Codes; 3.4 Another Family of Non-additive MRD Codes; 3.5 Some Concluding Remarks; References. Generalizing Subspace Codes to Flag Codes Using Group Actions1 Introduction; 2 Preliminaries; 2.1 The Network Model for Subspace Codes; 2.2 Matricial Representation of Subspaces; 2.3 Subspace Codes; 3 Group Actions; 4 Flags; 4.1 Cells and the Gaussâ#x80;#x93;Jordan Decomposition; 4.2 Circles, Sm-valued Distance and the Gaussâ#x80;#x93;Bruhat Decomposition; 4.3 Length and Depth of a Permutation and Corresponding Distance Functions; 4.4 Non-full Flags; 5 Flag Codes; 5.1 The Network Model for Flag Codes; 5.2 Sphere Sizes and the ell- `3Ì#x81;9`42`""Ì#x87;613A``45`47`""603Amathfrakdp Polynomial; References. Multi-shot Network Coding1 Introduction; 2 Preliminaries; 2.1 One-Shot Network Coding; 2.2 Convolutional Codes; 3 Multi-shot Network Coding; 3.1 Encoder and Decoder; 3.2 Channel Model; 3.3 Distances; 4 Rank Metric Convolutional Codes; 4.1 General Framework; 4.2 Usual Approach; 5 Concatenation Codes; References; Finite Geometries and Subspace Designs; Geometrical Aspects of Subspace Codes; 1 Introduction; 2 Preliminaries; 2.1 Codes in Projective Spaces; 3 Johnson Bound and Partial Spreads in Finite Projective Spaces; 3.1 The Johnson Bound and Partial Spreads. 3.2 Subspace Codes from Maximum Rank Distance Codes3.3 Planes in PG(5, q) Pairwise Intersecting in at Most a Point; 3.4 Planes in PG(5, q) Pairwise Intersecting in at Most a Point (Alternative Construction); 3.5 Solids in PG(7, q) Pairwise Intersecting in at Most a Line; 4 Optimal Mixed-Dimension Subspace Codes in PG(4, q); 5 Geometrical Links to Non-linear Maximum Rank Distance Codes; 5.1 The Case n=2; 5.2 The Case n=3; References; Partial Spreads and Vector Space Partitions; 1 Introduction; 2 Bounds and Constructions for Partial Spreads; 3 qr-divisible Sets and Codes.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 003/.54; Engineering; Coding theory; Computer networks; SCIENCE -- System Theory; TECHNOLOGY & ENGINEERING -- Operations Research; Coding theory; Computer networks; Engineering; Communications Engineering, Networks; Coding and Information Theory; Information Storage and Retrieval; Combinatorics; Computers -- Information Theory; Computers -- System Administration -- Storage & Retrieval; Mathematics -- Combinatorics; Coding theory & cryptology; Information retrieval; Combinatorics & graph theory; Telecommunication; Information storage and retrieva; Combinatorics; Technology & Engineering -- Telecommunications; Communications engineering / telecommunications; Electronic books
• Languages: English
• ISBNs: 9783319702933; 3319702939
• Related ISBNs: 9783319702926; 3319702920
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (SpringerLink, viewed February 8, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.