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MacWilliams' Extension Theorem for Bi-Invariant Weights over Finite Principal Ideal Rings [PDF]

, 2013
A finite ring R and a weight w on R satisfy the Extension Property if every R-linear w-isometry between two R-linear codes in R^n extends to a monomial transformation of R^n that preserves w.
Fadden, Cathy Mc +4 more
core

New extremal binary self-dual codes of length 68 via short kharaghani array over f_2 + uf_2 [PDF]

, 2016
In this work, new construction methods for self-dual codes are given. The methods use the short Kharaghani array and a variation of it. These are applicable to any commutative Frobenius ring.
Kaya, Abidin
core +2 more sources

Projective divisible binary codes [PDF]

, 2017
For which positive integers $n,k,r$ does there exist a linear $[n,k]$ code $C$ over $\mathbb{F}_q$ with all codeword weights divisible by $q^r$ and such that the columns of a generating matrix of $C$ are projectively distinct? The motivation for studying
Heinlein, Daniel +4 more
core +1 more source

On Double Cyclic Codes over Finite Chain Rings for DNA Computing. [PDF]