Optimal Linear Codes Over the Field of Order 7

We construct some new linear codes over the field of order 7 to determine the exact value of the minimum length for which a linear code of dimension four with given minimum weight exists for some open cases. Most of the new codes are constructed as projective duals of some 7-divisible codes from som...

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Bibliographic Details
Published in:2020 Algebraic and Combinatorial Coding Theory (ACCT) pp. 113 - 117
Main Authors: Nomura, Keita, Maruta, Tatsuya
Format: Conference Proceeding
Language:English
Published: IEEE 11.10.2020
Subjects:
divisible code
Information theory
linear code
Linear codes
Orbits
projective dual
Space vehicles
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Summary:We construct some new linear codes over the field of order 7 to determine the exact value of the minimum length for which a linear code of dimension four with given minimum weight exists for some open cases. Most of the new codes are constructed as projective duals of some 7-divisible codes from some orbits of a projectivity in the projective space.
DOI:10.1109/ACCT51235.2020.9383246