A note on the weight spectrum of the Schubert code Cα(2,m)

We consider the Schubert code C α ( 2 , m ) associated to the F q -rational points of the Schubert variety Ω α ( 2 , m ) in the Grassmannian G 2 , m . A correspondence between codewords of C α ( 2 , m ) and skew-symmetric matrices of certain special form is given. Using this correspondence, we give...

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Bibliographic Details
Published in:Designs, codes, and cryptography codes, and cryptography, 2018-12, Vol.86 (12), p.2825-2836
Main Authors: Piñero, Fernando L., Singh, Prasant
Format: Article
Language:English
Subjects:
Circuits
Coding and Information Theory
Computer Science
Cryptology
Data Structures and Information Theory
Discrete Mathematics in Computer Science
Information and Communication
Mathematical analysis
Matrix methods
Weight
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Summary:We consider the Schubert code C α ( 2 , m ) associated to the F q -rational points of the Schubert variety Ω α ( 2 , m ) in the Grassmannian G 2 , m . A correspondence between codewords of C α ( 2 , m ) and skew-symmetric matrices of certain special form is given. Using this correspondence, we give a formula for all possible weights of codewords in C α ( 2 , m ) . It is shown that the weight of each codeword is divisible by certain power of q . Further, a formula for the weight spectrum of the Schubert code C α ( 2 , m ) is given.
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-018-0477-2