Minimum distance of symplectic Grassmann codes
Copyright policy )Minimum distance of symplectic Grassmann codes
We introduce the Symplectic Grassmann codes as projective codes defined by symplectic Grassmannians, in analogy with the orthogonal Grassmann codes introduced in [4]. Note that the Lagrangian-Grassmannian codes are a special class of Symplectic Grassmann codes. We describe the weight enumerator of the Lagrangian--Grassmannian codes of rank $2$ and $3$ and we determine the minimum distance of the line Symplectic Grassmann codes.
Revised contents and biblography
- Università degli Studi di Brescia Italy
- University of Siena Italy
- University of Brescia Italy
FOS: Computer and information sciences, symplectic Grassmannian, Computer Science - Information Theory, Information Theory (cs.IT), Symplectic Grassmannian, Lagrangian Grassmannian code, Dual polar space, 94B05, 51A50, Polar geometry, symplectic spaces, orthogonal spaces, Linear codes and caps in Galois spaces, Incidence structures embeddable into projective geometries, Symplectic Grassmannian, Dual polar space, Error correcting code, Lagrangian Grassmannian code, dual polar space, FOS: Mathematics, Error correcting code, Mathematics - Combinatorics, Combinatorics (math.CO), Symplectic Grassmannian; Dual polar space; Error correcting code; Lagrangian Grassmannian code, Linear codes (general theory), error correcting code
FOS: Computer and information sciences, symplectic Grassmannian, Computer Science - Information Theory, Information Theory (cs.IT), Symplectic Grassmannian, Lagrangian Grassmannian code, Dual polar space, 94B05, 51A50, Polar geometry, symplectic spaces, orthogonal spaces, Linear codes and caps in Galois spaces, Incidence structures embeddable into projective geometries, Symplectic Grassmannian, Dual polar space, Error correcting code, Lagrangian Grassmannian code, dual polar space, FOS: Mathematics, Error correcting code, Mathematics - Combinatorics, Combinatorics (math.CO), Symplectic Grassmannian; Dual polar space; Error correcting code; Lagrangian Grassmannian code, Linear codes (general theory), error correcting code
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