A new class of optimal optical orthogonal codes with weight five

作者：Ma SK^*; Chang YX

来源：IEEE Transactions on Information Theory, 2004, 50(8): 1848-1850.

DOI：10.1109/TIT.2004.831845

• cyclic packing
• difference matrix (DM)
• g-regular
• optical orthogonal code (OOC)
• optimal

A (v, k, 1) optical orthogonal code (OOC), or briefly a (v, k, 1)-OOC, C, is a family of (0, 1) sequences of length v and weight k satisfying the following two properties:
1) Sigma(0less than or equal totless than or equal tov-1)x(t)x(t+i) less than or equal to 1 for any x = (x(0), x(1), ..., x(v-1)) is an element of C and any integer inot equivalent to 0 (mod v);
2) Sigma(0less than or equal totless than or equal tov-1)x(t)y(t+i) less than or equal to 1 for any x = (x(0), x(1), ..., x(v-1)) is an element of C, y = (y(0), y(1), ..., y(v-1)) is an element of C with x not equal y, and any integer i,
where the subscripts are reduced modulo v.A (v, k, 1)-OOC is optimal if it contains [(v - 1)/k(k - 1)] codewords. In this note, we establish that there exists an optimal (3(s)5 v, 5, 1)-OOC for any nonnegative integer s whenever v is a product of primes congruent to 1 modulo 4. This improves the known existence results concerning optimal OOCs.

• 出版日期2004-8
• 单位北京交通大学