Quantum Codes Constructed from Self-Dual Codes and Maximal Self-Orthogonal Codes Over F5

Self-dual and maximal self-orthogonal codes over F7

In this note, we give the classi5cation of self-dual F7-codes of length 12 and maximal self-orthogonal codes of lengths 10; 11 and 13. It is also shown that there is no self-dual [16; 8; d¿ 8] code over F7. c © 2002 Elsevier Science B.V. All rights reserved.

On self-dual codes over F5

The purpose of this paper is to improve the upper bounds of the minimum distances of self-dual codes over F5 for lengths 22, 26, 28, 32 − 40. In particular, we prove that there is no [22, 11, 9] self-dual code over F5, whose existence was left open in 1982. We also show that both the Hamming weight enumerator and the Lee weight enumerator of a putative [24, 12, 10] self-dual code over F5 are un...

Cyclic Codes and Self-Dual Codes Over

We introduce linear cyclic codes over the ring F 2 + uF 2 = f0; 1; u; u = u + 1g, where u = 0 and study them by analogy with the Z4 case. We give the structure of these codes on this new alphabet. Self-dual codes of odd length exist as in the case of Z4-codes. Unlike the Z4 case, here free codes are not interesting. Some nonfree codes give rise to optimal binary linear codes and extremal self-d...

Self-Dual Codes over Z_2xZ_4

Self-dual codes over Z2 ×Z4 are subgroups of Z2 ×Zβ4 that are equal to their orthogonal under an inner-product that relates to the binary Hamming scheme. Three types of self-dual codes are defined. For each type, the possible values α, β such that there exist a code C ⊆ Z 2 ×Z 4 are established. Moreover, the construction of a Z2Z4-linear code for each type and possible pair (α, β) is given. Fi...

Orthogonal designs and MDS self-dual codes