Construction for both self-dual codes and LCD codes

نویسندگان

چکیده

From a given [n, k] code C, we give method for constructing many codes C' such that the hull dimensions of C and are identical. This can be applied to constructions both self-dual linear complementary dual (LCD short). Using method, construct 661 new inequivalent extremal doubly even [56, 28, 12] codes. Furthermore, LCD by improve some previously known lower bounds on largest minimum weights binary length 26 ≤ n 40.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Double circulant self-dual and LCD codes over Galois rings

This paper investigates the existence, enumeration and asymptotic performance of self-dual and LCD double circulant codes over Galois rings of characteristic p and order p with p and odd prime. When p ≡ 3 (mod 4), we give an algorithm to construct a duality preserving bijective Gray map from such a Galois ring to Z p2 . Using random coding, we obtain families of asymptotically good self-dual an...

متن کامل

An Efficient Construction of Self-Dual Codes

We complete the building-up construction for self-dual codes by resolving the open cases over GF (q) with q ≡ 3 (mod 4), and over Zpm and Galois rings GR(p, r) with an odd prime p satisfying p ≡ 3 (mod 4) with r odd. We also extend the buildingup construction for self-dual codes to finite chain rings. Our building-up construction produces many new interesting self-dual codes. In particular, we ...

متن کامل

Construction of new extremal self-dual codes

In this paper, new binary extremal self-dual codes are presented. A number of new extremal singly-even self-dual codes of lengths 48; 64 and 78, and extremal doubly-even self-dual codes of lengths 80 and 88, are constructed. We also relate an extremal doubly-even self-dual code of length divisible by 24 to an extremal singly-even self-dual code of that length. New singly-even self-dual codes of...

متن کامل

Construction of Self - Dual Codes over F

We present two kinds of construction methods for self-dual codes over F2 + uF2. Specially, the second construction (respectively, the first one) preserves the types of codes, that is, the constructed codes from Type II (respectively, Type IV) is also Type II (respectively, Type IV). Every Type II (respectively, Type IV) code over F2 + uF2 of free rank larger than three (respectively, one) can b...

متن کامل

Construction of quasi-cyclic self-dual codes

There is a one-to-one correspondence between l-quasi-cyclic codes over a finite field Fq and linear codes over a ring R = Fq[Y ]/(Y m − 1). Using this correspondence, we prove that every l-quasi-cyclic self-dual code of length ml over a finite field Fq can be obtained by the building-up construction, provided that char (Fq) = 2 or q ≡ 1 (mod 4), m is a prime p, and q is a primitive element of F...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Advances in Mathematics of Communications

سال: 2023

ISSN: ['1930-5346', '1930-5338']

DOI: https://doi.org/10.3934/amc.2021070